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THE 



ENCYCLOPEDIA BRITANNICA 



ELEVENTH EDITION 



FIRST 


edit! 


on, 


published 


n three volumes, 


1768- 


-1771. 


SECOND 


» 




,, 


ten 


>> 


1777- 


-1784. 


THIRD 


> 






, 


eighteen 


» 


1788- 


-1797. 


FOURTH 


> 






y 


twenty 


»> 


1801- 


-1810. 


FIFTH 


> 






j 


twenty 


» 


1815- 


-1817. 


SIXTH 


* 






, 


twenty 


»» 


1823- 


-1824. 


SEVENTH 


» 






> 


twenty-one 


>» 


1830- 


-1842. 


EIGHTH 


» 






» 


twenty-two 


>> 


1853- 


-i860 


NINTH 


> 






7 


twenty-five 


>j 


1875- 


-1889. 


TENTH 


9 




ninth ed 


ition and eleven 












supplementary volumes, 




1902- 


-1903. 


ELEVENTH 


> 


> 


pub] 


ished 


in twenty-nine volumes, 


1910 — 1911, 



COPYRIGHT 

in all countries subscribing to the 

Bern Convention 

by 

THE CHANCELLOR, MASTERS AND SCHOLARS 

of the 
UNIVERSITY OF CAMBRIDGE 



All rights reserved 



THE 

ENCYCLOPEDIA BRITANNICA 

A 

DICTIONARY 

OF 

ARTS, SCIENCES, LITERATURE AND GENERAL 

INFORMATION 



ELEVENTH EDITION 



VOLUME XIV 

HUSBAND to ITALIC 



New York 

Encyclopaedia Britannica, Inc. 
342 Madison Avenue 



Copyright, in the United States of America, 191 1, 

by 

The Encyclopaedia Britannica Company. 



INITIALS USED IN VOLUME XIV. TO IDENTIFY INDIVIDUAL 

CONTRIBUTORS, 1 WITH THE HEADINGS OF THE 

ARTICLES IN THIS VOLUME SO SIGNED. 



A* lift* 


A. 


Bo.* 


A. 


Cy. 


A. 


C. G 



Adolfo Bartoli (1833-1894). f 

Formerly Professor of Literature at the Istituto di studi superior! at Florence. "1 Italian Literature (in part). 



A. E. G.* 



A. E. H. L. 



A. F. C. 



A. G. 



A. 


Ge. 


A. 


Go.* 


A. 


G. G. 


A. 


H.-S. 


A. 


M. C. 


A. 


N. 


A. 


So. 


A 


S. Wo. 


A 


. W. H.* 


A 


. W. Po. 



Honorary Canon of 



Author of Sto in delta letter atura Italiana; &c. 

Augxiste Boudinhon, D.D., D.C.L. 

Professor of Canon Law at the Catholic University of Paris. 
Paris. Editor of the Canonists contemporain. 

Arthur Ernest Cowley, M.A., Litt.D. 

Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen College. 

Albert Charles Lewis Gotthilf Gunther, M.A., M.D., Ph.D., F.R.S. 

Keeper of Zoological Department, British Museum, 1875-1895. Cold Medallist, 
Royal Society, 1878. Author of Catalogues of Colubrine Snakes, Balrachia Salientia, - 
and Fishes in the British Museum ; Reptiles of British India ; Fishes of Zanzibar ; 
Reports on the " Challenger " Fishes; &c. 

Rev. Alfred Ernest Garvie, M.A., D.D. 

Principal of New College, Hampstead. Member of the Board of Theology and the . 
Board of Philosophy, London University. Author of Studies in the inner Life 
of Jesus ; &c. 

Augustus Edward Hough Love, M.A., D.Sc, F.R.S. 

Sedleian Professor of Natural Philosophy in the University of Oxford. Hon. _ 
Fellow of Queen's College, Oxford ; formerly Fellow of St John's College, Cambridge. 
Secretary to the London Mathematical Society. 

Alexander Francis Chamberlain, A.M., Ph.D. 

Assistant Professor of Anthropology, Clark University, Worcester, Massachusetts. . 
Member of American Antiquarian Society; Hon. Member of American Folk-lore 
Society. Author of The Child and Childhood in Folk Thought. 

Major Arthur George Frederick Griffiths (d. 1908). 

H.M. Inspector of Prisons, 1878-1896. Author of The Chronicles of Newgale; 
Secrets of the Prison House ; &c. 

Sir Archibald Geikie, LL.D. 

See the biographical article, Geikie, Sir A. 

Rev. Alexander Gordon, M.A. 

Lecturer on Church History in the University of Manchester. 

Sir Alfred George Greenhill, M.A., F.R.S. 

Formerly Professor of Mathematics in the Ordnance College, Woolwich. Author 
of Differential and Integral Calculus with Applications; Hydrostatics; Notes on 
Dynamics ; &c. 

Sir A. Houtum-Schindler, CLE. 

General in the Persian Army. Author of Eastern Persian Irak. 

Agnes Mary Clerke. 

See the biographical article, Clerke, A. M. 

Alfred Newton, F.R.S. 

See the biographical article, Newton, Alfred. 

Albrecht Socin, Ph.D. (184.4-1899). 

Formerly Professor of Semitic Philology in the Universities of Leipzig and Tubingen. 
Author of Arabische Grammatik; &c. 

Arthur Smith Woodward, LL.D., F.R.S. 

Keeper of Geology, Natural History Museum, South Kensington. Secretary of 
the Geological Society, London. 

Arthur -William Holland. 

Formerly Scholar of St John's College, Oxford. Bacon Scholar of Gray's Inn, 
1900. 

Alfred William Pollard, M.A. 

Assistant Keeper of Printed Books, British Museum. Fellow of King's College, 
London. Hon. Secretary Bibliographical Society. Editor of Books about Books 
and Bibliographica. Joint-editor of The Library. Chief Editor of the " Globe " 
Chaucer. 



Index Librorum Prohl- 
bitorum; Infallibility. 

f Ibn Gabirol; 

\ Inscriptions: Semitic. 



Ichthyology (in part). 



Immortality; 
Inspiration. 



Infinitesimal Calculus. 



Indians, North American. 



-! Identification. 

\ Hutton, James. 
\ Illuminati. 

\ Hydromechanics. 



-j Isfahan (in part). 
-j Huygens, Christiaan. 
\ Ibis; Icterus. 



Irak-Arabi (in pari). 

( Ichthyosaurus; 
1 Iguanodon. 

Imperial Cities; 
Instrument of Government 



Incunabula. 



tk» W. K. 



Alexander Wood Renton, M.A., LL.B. J Inebriety, Law of; 

Puisne Judge of the Supreme Court of Ceylon. Editor of Encyclopaedia of the~] i ns anity: Law. 
Laws of England. *- 

1 A complete list, showing all individual contributors, appears in the final volume. 



VI 




CP.A. 


ao. 




C. H. 


Ha. 


C. LI 


M. 


C. R. 


B. 



INITIALS AND HEADINGS OF ARTICLES 



c.s.* 

C. T.L. 

C. We. 

D. B. Ma. 

D. G. H. 

D. H. 
D. P. T. 

D. S. M. 

E. A. M. 
E.Br. 



E. 


Bra. 


E. 


C. B. 


E. 


C. Q. 


E. 


P.S. 


E. 


P. S.D 


E. 


G. 


E 


Htt. 


E 


H. B. 


E 


. H. M. 


E 


. H. P. 



Charles Francis Atkinson. J Infantry; 

Formerly Scholar of Queen's College, Oxford. Captain, 1st City of London (Royal | Julian Wars. 
Fusiliers). Author of The Wilderness and Cold Harbour. 

Colonel Charles Grant. 

Formerly Inspector of Military Education in India. 

Carlton Huntley Hayes, A.M., Ph.D. 

Assistant Professor of History at Columbia University, New York City, 
of the American Historical Association. 



{ 



India: Costume. 



Member! Innocent V., VIII. 



J Instinct; 
Principal of University College, | Inte lligence in Animals, 



Ibn Batuta 
Iclrisi. 



part) ; 



| Italian Language {in pari). 
Insurance {in part). 



Barrister-at-Law, Inner Temple. 



Infant Schools. 



Author J 
Theory ; j 



Imam. 



Ionia {in 
Isauria. 



part); 



Author of Short History of Royal 1 Impressment, 



Instrumentation. 



Conway Lloyd Morgan, LL.D., F.R.S. 

Professor of Psychology at the University of Bristol. 

Bristol, 1887-1909. Author of Animal Life and Intelligence; Habit and Instinct. 

Charles Raymond Beazley, M.A., D.Litt., F.R.G.S., F.R.Hist.S. 

Professor of Modern History in the University of Birmingham. Formerly Fellow 
of Merton College, Oxford; and University Lecturer in the History of Geography. 
Lothian Prizeman, Oxford, 1889. Lowell ^ Lecturer, Boston, 1908. Author of 
Henry the Navigator; The Dawn of Modern Geography; &c. 
Carlo Sat.viont. 

Professor of Classical and Romance Languages, University of Milan. 

Charlton Thomas Lewis, Ph.D. (1834-1904}. 

Formerly Lecturer on Life Insurance, Harvard and Columbia Universities, and on. 
Principles of Insurance. Cornell University. Author of History of Germany; Essays; 
Addresses; &c. 

Cecil Weatherly. 

Formerly Scholar of Queen's College, Oxford. 

Duncan Black Macdonald, M.A., D.D. 

Professor of Semitic Languages, Hartford Theological Seminary, U.S.A. 
of Development of Muslim Theology, Jurisprudence and Constitutional 
Selection from Ibn Khaldum; Religious Attitude and Life in Islam; &c. 

Davtd George Hogarth, M.A. 

Keeper of the Ashmolean Museum, Oxford. Fellow of Magdalen College, Oxford. 
Fellow of the British Academy. Excavated at Paphos, 1888; Naucratis, 1 899 and - 
1903; Ephesus, 1904-1905; Assiut, 1906-1907; Director, British School at Athens. 
1897-1900; Director, Cretan Exploration Fund, 1899. 

David Hannay. 

Formerly British Vice-Consul at Barcelona. 
Navy, 1 217-1688; Life of Emilio Castelar; &c. 

Donald Francis Tovey. _ . 

Author of Essays in Musical Analysis; comprising The Classical Concerto, The 
Goldberg Variations, and analyses of many other classical works. 

Dugald Sutherland MacColl, M.A., LL.D. f 

Keeper of the National Gallery of British Art (Tate Gallery). Lecturer on the History J Impressionism. 

of Art, University College, London; Fellow of University College, London, j 

Author of Nineteenth Century Art; &c. L 

Edward Alfred Minchin, M.A., F.Z.S. f 

Professor of Protozoology in the University of London. Formerly Fellow of Merton J ny° r 0meausae; 

College, Oxford ; and Lecturer on Comparative Anatomy in the University of Oxford, j Hydrozoa. 

Author of " Sponges and Sporozoa " in Lankester's Treatise on Zoology; &c. *~ 

Erjtest Barker, M.A. f 

Fellow and Lecturer in Modern History, St John's College, Oxford. Formerly -\ Imperial Chamber. 

Fellow and Tutor of Merton College. Craven Scholar, 1895. . I 

Edwin Bramwell, M.B., F.R.C.P., F.R.S. (Edin.). f 

Assistant Physician, Royal Infirmary, Edinburgh. -^Hysteria {in part). 

Right Rev. Edward Cuthbert Butler, O.S.B., D.Litt. r 

AbDot of Downside Abbey, Bath. An+tiru- n( " The. I ^,1=1^ H,"ctr,^i, ,-,f Polios;, ,.= " J 
in Cambridge Texts and Studies. 

Edmund Crosby Quiggin, M.A. 

Fellow, Lecturer in Modern History, and Monro Lecturer in Celtic, Gonville and -i Ireland: Early History. 
Caius College, Cambridge. 

Edward Fairbrother Strange. 

Assistant Keeper, Victoria and Albert Museum, South Kensington. 
Council, Japan Society. Author of numerous works on art subjects, 
of Bell's " Cathedral " Series. 

Lady Dilke. 

See the biographical article: Dilke, Sir C. W., Bart. 

Edmund Gosse, LL.D. 

See the biographical article, Gosse, Edmund. 

EMIL HUBNER. 

See the biographical article, Hubner, Emil. 

Sir Edward Herbert Bunbury, Bart., M.A., F.R.G.S. (d. 1895). f 

M.P. for Bury St Edmunds, 1 847-1 852. Author of a History of Ancient Geography; \ Ionia {in part).- 
&c. L 



Author of " The Lausiac History of Palladius " i Imitation of Christ. 



Member of J Illustration: Technical 
Joint-editor | Developments. 



\ Ingres. 

f Huygen 

\ Ibsen; '. 

\ Inscriptions: Latin {in pari). 



("Huygens, Sir Constantijn; 
1 Ibsen; Idyl. 



Ellis Hovell Minns, M.A. 

Lecturer and Assistant Librarian, and formerly Fellow, Pembroke College, Cambridge 
University Lecturer in Palaeography. 

Edward Henry Palmer, M.A. 

See the biographical article, Palmer, E. H. 



Iazyges; Issedones. 
Ibn Khaldun [in part). 



INITIALS AND HEADINGS OF ARTICLES 



Vll 



E, K. 

E. L.H. 

Ed. M. 
E. M. T. 



E.O.* 

F. A. F. 

F. C. C. 

F. G. M. B. 
F. J. H. 

F. LI. G. 



F. 


P.* 


F. 


S.P. 


F. 


Wa. 


F. 


W. R.* 


F. 


Y. P. 


G 


A. B. 



G. A. Gr. 

G. A. J. C. 

G. B. 
G. F. H.* 

G. G. Co. 

3. H. C. 



Edmund Knecht, Ph.D., M.Sc.TECH.(Manchester), F.I.C. 

Professor of Technological Chemistry, Manchester University. Head of Chemical 
Department, Municipal School of Technology, Manchester. Examiner in Dyeing, " 
City and Guilds of London Institute. Author of A Manual of Dyeing; &c. Editor 
of Journal of the Society of Dyers and Colourisls. 

The Right Rev. the Bishop of Lincoln (Edward Lee Hicks). 

Honorary Fellow of Corpus Christi College, Oxford. Formerly Canon Residentiary, 
of Manchester. Fellow and Tutor of Corpus Christi College. Author of Manual 
of Greek Historical Inscriptions ; &c. 

Eduard Meyer, Ph.D., D.Lrrr.(Oxon.), LL.D. * 

Professor of Ancient History in the University of Berlin. Author of Geschichte des ~ 
Alterthums ; Geschichte des alien Aegyptens; Die Israelilen und ihre Nachbarsldmme. 

Sir Edward Maunde Thompson, G.C.B., I.S.O., D.C.L., Litt.D., LL.D. 

Director and Principal Librarian, British Museum, 1 898-1 909. Sandars Reader 
in Bibliography, Cambridge, 1895-1896. Hon. Fellow of University College, 
Oxford. Correspondent of the Institute of France and of the Royal Prussian . 
Academy of Sciences. Author of Handbook of Greek and Latin Palaeography. 
Editor of Chronicon Angliae. Joint-editor of publications of the Palaeographical 
Society, the New Palaeographical Society, and of the Facsimile of the Laurentian 
Sophocles. 

Edmund Owen, M.B., F.R.C.S., LL.D., D.Sc. 

Consulting Surgeon to St Mary's Hospital, London, and to the Children's Hospital, . 
Great Ormond Street; late Examiner in Surgery at the Universities of Cambridge, 
Durham and London. Author of A Manual of Anatomy for Senior Students. 

Frank Albert Fetter, Ph.D. 

Professor of Political Economy and Finance, Cornell University. Member of the 
State Board of Charities. Author of The Principles of Economics; &c. 

Frederick C'ornwallis Conybeare, M.A., D.TH.(Giessen). 

Fellow of the British Academy. Formerly Fellow of University College, Oxford. 
Author of The Ancient Armenian Texts of Aristotle; Myth, Magic and Morals; &c. 

Frederick George Meeson Beck, M.A. 

Fellow and Lecturer in Classics, Clare College, Cambridge. 

Francis John Haverfield, M.A., LL.D., F.S.A. 

Camden Professor of Ancient History in the University of Oxford. Fellow of 
Brasenose College. Fellow of the British Academy. Formerly Censor, Student, - 
Tutor and Librarian of Christ Church, Oxford. Ford's Lecturer, 1906-1907. 
Author of Monographs on Roman History, especially Roman Britain; &c. 

Francis Llewellyn Griffith, M.A., Ph.D., F.S.A. 

Reader in Egyptology, Oxford University. Editor of the Archaeological Survey 
and Archaeological Reports of the Egypt Exploration Fund. Fellow of Imperial 
German Archaeological Institute. 

Frederick Peterson M.DPh.D j Insanity: Hospital 

Professor of Psychiatry, Columbia University. President of New York State ^ r 

Commission in Lunacy, 1902-1906. Author of Mental Diseases; &c. 

Francis Samuel Philbrick, A.M., Ph.D. 

Formerly Fellow of Nebraska State University, and Scholar and Resident Fellow of 
Harvard University. Member of American Historical Association. 



Indigo. 



Inscriptions: Greek 

{in pari). 



Hystaspes; Iran. 



Illuminated MSS. 



Hydrocephalus. 

Interstate Commerce. 

j Iconoclasts; 
[Image Worship. 

j Hwicce. 
Icknield Street. 



Hyksos; Isis. 



I Treatment. 



Independence, 
Declaration of. 



Francis Watt, M.A. 

Barrister-at-Law, Middle Temple. Author of Law's Lumber Room. 

Frederick William Rudler, I.S.O., F.G.S. 

Curator and Librarian of the Museum of Practical Geology, London, 1879-1902. 
President of the Geologists' Association, 1 887-1 889. 

Frederick York Powell, D.C.L., LL.D. 

See the biographical article, Powell, Frederick York. 

George A. Boulenger, F.R.S., D.Sc, Ph.D. 

In charge of the collections of Reptiles and Fishes, Department of Zoology, British 
Museum. Vice-President of the Zoological Society of London. 

George Abraham Grierson, CLE., Ph.D., D.Litt. (Dublin). 

Member of the Indian Civil Service, 1873-1903. In charge of Linguistic Survey 
of India, 1898-1902. Gold Medallist, Royal Asiatic Society, 1909. Vice-President 
of the Royal Asiatic Society. Formerly Fellow of Calcutta University. Author 
of The Languages of India ; &c. 

Grenville Arthur James Cole. r 

Director of the Geological Survey of Ireland. Professor of Geology, Royal College -j 
of Science for Ireland, Dublin. Author of Aids in Practical Geology; &c. I 

Sir George Christopher Molesworth Birdwood, K.C.I.E. f 

See the biographical article, Birdwood, Sir G. C. M. ^ 

George Francis Hill, M.A. 

Assistant in Department of Coins and Medals, British Museum. Author of 
Sources for Greek History 478-431 B.C.; Handbook of Greek and Roman Coins; &c. 

George Gordon Coulton, M.A. 

Birkbeck Lecturer in Ecclesiastical History, Trinity College, Cambridge, 
of Medieval Studies; Chaucer and his England; &c. 



Inn and Innkeeper. 



Hyacinth; Iolite. 



r 

i 

{ 

f Iceland: History, and 
l Ancient Literature. 

Ichthyology {in part). 

Indo-Aryan Languages. 

Ireland: Geology. 
Incense. 

Inscriptions: Greek 

{in part). 

Author-! Indulgence. 



Gf.org;; Herbert Carpenter, B.Sc. (Lond.). 

Professor of Zoology in the Royal College of Science, Dublin. 
their Structure and Life. 



Author of Insects: 



Hymenoptes^g 

Ichneumon-Fly; 

Insect. 



Vlll 



INITIALS AND HEADINGS OF ARTICLES 



G. I. A. 
G.J. 

G. K. 
G. P. M. 
G. W. K. 



G. W. T. 



H. Ch. 



H. C. R. 



H. 


L. 


H. 


H. 


M. 


H. 


H. 


N. 


B. 


H 


0. 




H. 


St. 




H. 


T. 


A. 


H 


y. 




I. 


A. 





J. A. P. 



J. Bs. 



J. B. T. 



GRA/ Senator L ot S th e L Kingdom of Italy. Professor of Comparative Grammar at the! Italian Language (in part). 
University of Milan. Author of Codice Islandese; &c. I 

George Jamieson, C.M.G., M.A. J 

Formerly Consul-General at Shanghai, and Consul and Judge of the Supreme Court, 1 Hwang HO. 
Shanghai. ^- 

Gustav Kruger, Ph.D. f 

Professor of Church History in the University of Giessen. Author of Das Papstthum ; i lrenaeus. 
&c. <- 

George Percival Mudge, A.R.C.S., F.Z.S. 

Lecturer on Biology, London Hospital Medical College, and London School of * 
Medicine for Women, University of London. Author of A Text Book of Zoology ; &c. 

Very Rev. George William Kitchin, M.A., D.D., F.S.A. 

Dean of Durham, and Warden of the University of Durham. Hon. Student of - 
x Christ Church, Oxford. Fellow of King's College, London. Dean of Winchester, 
1883-1894. Author of A History of France; &c. 



Incubation and Incubators. 



Rev. Griffithes Wheeler Thatcher, M.A., B.D. 

Warden of Camden College, Sydney, N.S.W. Formerly Tutor in Hebrew and Old 
Testament History at Mansfield College, Oxford. Author of a Commentary on 
Judges; An Arabic Grammar; &c. 



Hutten, Ulrieh von. 

Ibn 'Abd Rabbihi; 
Ibn 'Arabi; Ibn Athlr; 
Ibn Duraid; Ibn Farad!; 
Ibn Farid; Ibn Hazm; 
Ibn Hisham; Ibn Ishaq; 
Ibn Jubair; Ibn Khaldun 

(in part); 
Ibn Khallikan; 
Ibn Qutaiba; Ibn Sa'd; 
Ibn fufail; Ibn Usaibi'a; 
Ibrahim Al-MausUT. 

Iron Mask; Ismail. 

1 

1 Isfahan: History. 

J Infancy; 

I Intestinal Obstruction. 



Iron and Steel. 



Hugh Chisholm, M.A. 

Formerly Scholar of Corpus Christi College, Oxford. Editor the 11th edition - 
of the Encyclopaedia Britannica; Co-editor of the 10th edition. 

Sir Henry Creswicke Rawlinson, Bart., K.C.B. 

See the biographical article, Rawlinson, Sir Henry Creswicke, 

Harriet L. Hennessv, M.D., (Brux.) L.R.C.P.I., L.R.C.S.I. 

Henry Marion Howe, A.M., LL.D. 

Professor of Metallurgy, Columbia University. Author of Metallurgy of Steel; &c. 

Henry Newton Dickson, M.A., D.Sc, F.R.G.S. J 

Professor of Geography, University College, Reading. Author of Elementary] Indian Ocean. 

Meteorology ; Papers on Oceanography; &c. *- 

Hermann Oelsner, M.A., Ph.D. f 

Taylorian Professor of the Romance Languages in University of Oxford. Member J xtalian Literature (in part). 
of Council of the Philological Soaety. Author of A History of Provencal Literature; 
&c. > 

Henry Sturt. M.A. \ induction. 

Author of Idola Thealri; The Idea of a Free Church; and Personal Idealism. I 

Rev. Herbert Thomas Andrews. f 

Professor of New Testament Exegesis, New College, London. Author of the J Ignatius. 
" Commentary on Acts " in the Westminster New Testament; Handbook on the ' 
Apocryphal Books in the " Century Bible." 



I 



Ibn Batuta (in part). 



%J. C. H. 
J. C. Van D. 



Sir Henry Yule, K.C.S.I., C.B. 

See the biographical article, Yule, Sir Henry. 

Israel Abrahams, M.A. 

Reader in Talmudic and Rabbinic Literature in the University of Cambridge. J Ibn Tlbbon; 

Formerly President, Jewish Historical Society in England. Author of A Short Immanuel Ben Solomon. 

History of Jewish Literature; Jewish Life in the Middle Ages; &c. *- 

John Ambrose Fleming, M.A., F.R.S., D.Sc. _ _ f 

Pender Professor of Electrical Engineering in the University of London. Fellow 
of University College, London. Formerly Fellow of St John's College, Cambridge, \ Induction Coil. 
and Lecturer on Applied Mechanics in the University. Author of Magnets and 
Electric Currents. \_ 

James Burgess, CLE., LL.D., F.R.S.(Edin-), F.R.G.S., Hon.A.R.I.B.A. r 

Formerly Director General of Archaeological Survey of India. Author of Archaeo- ! . M ArnhitontnrA 
logical Survey of Western India. Editor of Fergusson's History of Indian Archi-'\ MOJan Arcnueciure. 
lecture. I 

Sir Tohn Batty Tuke, Kt., M.D., F.R.S.(Edin.), D.Sc, LL.D. f „ .„.„ ,. . ,. 

President of the Neurological Society of the United Kingdom. Medical Director J HySiena \m part), 

of New Saughton Hall Asylum, Edinburgh. M.P. for the Universities of Edinburgh ] Insanity: Medical. 
and St Andrews, 1900-1910. *- 



Right Rev. John Cuthbert Hedley, O.S.B., D.D. J 

K.C. Bishop of Newport. Author of The Holy Eucharist; &c. 1 

John Charles Van Dyke. I 

Professor of the History of Art, Rutgers College, New Brunswick, N.J. Formerly < 
Editor of The Studio and Art Review. Author of Art for Art's Sake; History of 
Painting; Old. English Masters; &c. 



Immaculate Conception. 



Inness, George. 



INITIALS AND HEADINGS OF ARTICLES 



IX 



J. c. w. 

J. D. B. 

J. P. P. 
J. F.-K. 

J. G. K. 

J. G. Sc. 

J. H. A. H. 
J. H. Mu. 

J. H. Be. 

J. H. van't H. 
J. L. M. 

J. Mn. 

J. M. A. de L. 

J. M. M. 

J. P. E. 
J. P. Pe. 

J. S. Bl. 
J. S. Co. 

J. S. F. 

J. T. Be. 
J. V.* 
Jno. W. 



{ 



Inns of Court. 



James Claude Webster. 

Barrister-at-Law, Middle Temple. 

James David Bourchier, M.A., F.R.G.S. f 

King's College, Cambridge. Correspondent of The Times in South-Eastern Europe. J j on j an Islands. 
Commander of the Orders of Prince Danilo of Montenegro and of the Saviour of 
Greece, and Officer of the Order of St Alexander of Bulgaria. *- 



John Faithfull Fleet, CLE. Ph.D. 

Commissioner of Central and Southern Divisions of Bombay, 1891-1897. 
of Inscriptions of the Early Gupta Kings ; &c. 



Author j Inscriptions: 



Indian. 



Isla, J. F. de. 



James Fitzmaurice-Kelly, Litt.D., F.R.Hist.S. 

Gilmour Professor of Spanish Language and Literature, Liverpool University. 
Norman McColl Lecturer, Cambridge University. Fellow of the British Academy. ' 
Member of the Royal Spanish Academy. Knight Commander of the Order of 
Alphonso XII. Author of A History of Spanish Literature; &c. 

John Graham Kerr, M.A., F.R.S. f 

Regius Professor of Zoology in the University of Glasgow. Formerly Demonstrator J .. 

in Animal Morphology in the University of Cambridge. Fellow of Christ's College, 1 Ichthyology Km part). 

Cambridge, 1 898-1904. Walsingham Medallist, 1898. Neill Prizeman, Royal 

Society of Edinburgh, 1904. 

Sir James George Scott, K.C.I.E. j 

Superintendent and Political Officer, Southern Shan States. Author of Burma, 1 Irrawaddy. 
a Handbook ; The Upper Burma Gazetteer ; &c. <■ 

John Henry Arthur Hart, M.A. j Hyrcanus. 

Fellow, Theological Lecturer and Librarian, St John's College, Cambridge. I 

John Henry Muirhead, M.A., LL.D. f 

Professor of Philosophy in the University of Birmingham. Author of Elements^ Idealism. 
of Ethics ; Philosophy and Life ; &c. Editor of Library of Philosophy. I 

Very Rev. John Henry Bernard, M.A., D.D., D.C.L. f 

Dean of St Patrick's Cathedral, Dublin. Archbishop King's Professor of Divinity J , . , 

and formerly Fellow of Trinity College, Dublin. Joint-editor of the Irish Liber \ "eland, Lnurcn 01. 
Hymnorum ; &c. I 



Isomerism. 



Iberians; Ionians. 



Jacobus Henricus van't Hoff, LL.D., D.Sc, D.M. 

See the biographical article van't Hoff, Jacobus Henricus. 

John Lynton Myres, M.A., F.S.A., F.R.G.S. 

Wykeham Professor of Ancient History in the University of Oxford. Formerly . 
Gladstone Professor of Greek and Lecturer in Ancient Geography, University of 
Liverpool. Lecturer in Classical Archaeology in University of Oxford. 

John Macpherson, M.D. 

Formerly Inspector-General of Hospitals, Bengal. 

Jean Marie Antoine de Lanessan. 

See the biographical article, Lanessan, J. M. A. de. 

John Malcolm Mitchell. f 

Sometime Scholar of Queen's College, Oxford. Lecturer in Classics, East London <j Hyacinthus. 
College (University of London). Joint-editor of Grote's History of Greece. [ 

Jean Paul Hippolyte Emmanuel Adhemar Esmein. [ 

Professor of Law in the University of Paris. Officer of the Legion of Honour. __ 
Member of the Institute of France. Author of Cours elementaire d'histoire du droit 
francais ; &c. 

Rev. John Punnett Peters, Ph.D., D.D. 

Canon Residentiary, Cathedral of New York. Formerly Professor of Hebrew in 
the University of Pennsylvania. Director of the University Expedition to Baby- - 
Ionia, 1888-1895. Author of Nippur, or Explorations and Adventures on the 
Euphrates. I 

John Sutherland Black, M.A., LL.D. [ 

Assistant Editor of the 9th edition of the Encyclopaedia Britannica. Joint-editors HllSS, John. 
of the Encyclopaedia Biblica. \_ 



\ Insanity : Medical {in part) . 
\ Indo-China, French {in part). 



Intendant. 



Irak-Arabi {in part). 



India : Geography and 
Statistics {in part),' 
History {in part); 

Indore. 

Itacolumite. 



James Sutherland Cotton, M.A. 

Editor of the Imperial Gazetteer of India. Hon. Secretary of the Egyptian Explora- 
tion Fund. Formerly Fellow and Lecturer of Queen's College, Oxford. Author " 
of India; &c. 

John Smith Flett, D.Sc, F.G.S. 

Petrographer to the Geological Survey. Formerly Lecturer on Petrology in Edin- 
burgh University. Neill Medallist of the Royal Society of Edinburgh. Bigsby 
Medallist of the Geological Society of London. 1 

John Thomas Bealby. r 

Joint-author of Stanford's Europe. Formerly Editor of the Scottish Geographical \ Irkutsk {in part). 
Magazine. Translator of Sven Hedin's Through Asia, Central Asia and Tibet; &c. [ 

Jules Viard. c 

Archivist at the National Archives, Paris. Officer of Public Instruction, 
of La France sous Philippe VI. de Valois; &c. 

John Westlake, K.C., LL.D. 

Professor of International Law, Cambridge. 1888-1908. One of the Members for the f 
United Kingdom of International Court of Arbitration under the Hague Convention, I 
1900-1906. Bencher of Lincoln's Inn. Author of A Treatise on Private International i 
Law, or the Conflict of Laws: ChaW*r* on the Principles of International Law, pt. i. j 
" Peace," nt. ii. " War." ' 



Author X Isabella of Bavarfa. 



International Law: 

Private. 



X 

L, 

L. C. B. 
L. Ho. 
L. J. S, 

L. T. D. 



INITIALS AND HEADINGS OF ARTICLES 



Count Lutzow, Litt.D. (Oxon.), Ph.D. (Prague), F.R.G.S. 

Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hon. Member 
of the Royal Soeiety of Literature. Member of the Bohemian Academy; &c. 
Author of Bohemia, a Historical Sketch; The Historians of Bohemia (Ilchester 
Lecture, Oxford, 1904) ; The Life and Times of John Hus; &c. 

Lewis Campbell Bruce, M.D., F.R.C.P. 
Author of Studies in Clinical Psychiatry. 



Hussites. 



M. 


Ha. 




M. 


Ja. 




M. 


0. B. 


C. 


N. 


M. 




0. 


J. R. 


H. 


P. 


A. 




P. 


A. K 




P. 


CM. 





P. Gi. 

P. Sm. 
R. 

R. A. S. M. 

R. Ba. 

R.C.J. 
R. G. 
R. H. C. 

R. L.* 
R. P. S. 



Laurence Housman. 

See the biographical article, Housman, L. 

Leonard James Spencer, M.A. 

Assistant in Department of Mineralogy, British Museum. 
Sidney Sussex College, Cambridge, and Harkness Scholar. 

logical Magazine. 



\ Insanity: Medical {in part). 
\ Illustration {in part). 



Formerly Scholar of J 
Editor of the Minera- 1 



Hypersthene; Ilmenite. 



Sir Lewis Tonna Dibdin, M.A., D.C.L., F.S.A. 

Dean of the Arches; Master of the Faculties; and First Church Estates Commissioner. 
Bencher of Lincoln's Inn. Author of Monasticism in England; &c. 

Marcus Hartog, M.A., D.Sc, F.L.S. [ 

Professor of Zoology, University College, Cork. Author of " Protozoa " in Cam- -j Infusoria. 
bridge Natural History; and papers for various scientific journals. t 

Morris Jastrow, Jun., Ph.D. 



Incense: Ritual Use. 



Assistant Secretary of the J Ireland: Geography. 



Inquisition. 



Professor of Semitic Languages, University of Pennsylvania, U.S.A. Author of -! Ishtar. 
Religion of the Babylonians and Assyrians; &c. |_ 

Maximilian Otto Bismarck Caspari, M.A. r 

Reader in Ancient History at London University. Lecturer in Greek at Birmingham -J Irene (7 <;2-8cn) 
University, 1905-1908. [ ° 

Norman McLean, M.A. r 

Fellow, Lecturer and Librarian of Christ's College, Cambridge. University Lecturer j T,- aap _t AntinpJi 
in Aramaic. Examiner for the Oriental Languages Tripos and the Theological 1 Anuocn. 

Tripos at Cambridge. L 

Osbert John Radcliffe Howarth, M.A. 

Christ Church, Oxford. Geographical Scholar, 1901. 
British Association. 

Paul Daniel Alphandery. 

Professor of the History of Dogma, Ecole pratique des hautes etudes, Sorbonne, 
Paris. Author of Les Idees morales chez Us hMerodoxes latines au debut du XIII'. ' 
siecle. 

Prince Peter Alexeivitch Kropotkin. 

See the biographical article, Kropotkin, Prince P. A. 

Peter Chalmers Mitchell, M.A., F.R.S., F.Z.S., D.Sc, LL.D. 

Secretary to the Zoological Society of London. University Demonstrator in 
Comparative Anatomy and Assistant to Linacre Professor at Oxford, 1 888-1 891 
Examiner in Zoology to the University of London, 1903. Author of Outlines 
of Biology; &c. 

Peter Giles. M.A., LL.D., Litt.D. 

Fellow and Classical Lecturer of Emmanuel College, Cambridge, and University 
Reader in Comparative Philology. Formerly Secretary of the Cambridge Philo- 
logical Society. Author of Manual of Comparative Philology; &c. 

Preserved Smith, Ph.D. 

Rufus B. Kellogg Fellow, Amherst College, Amherst, Mass. 

The Right Hon. Lord Rayleigh. 

See the biographical article, Rayleigh, 3rd Baron. 



Irkutsk {in part). 



891-^ Hybridism. 



i; 

Indo-European 
Languages. 

Innocent I., II. 



J Interference of Light. 



Robert Alexander Stewart Macalister, M.A., F.S.A. 

St John's College, Cambridge. Director of Excavations for the Palestine Explora- 
tion Fund. 

Richard Bagwell, M.A., LL.D. 

Commissioner of National Education for Ireland. 
Tudor s ; Ireland under the Stuarts. 

Sir Richard Clavf.rhouse Jebb, D.C.L., LL.D. 

See the biographical article, Jebb, Sir Richard Claverhouse. 
Richard Garnett, LL.D. 

See the biographical article, Garnett, Richard. 



Idumaea. 



Author of Ireland under the \ Ireland: Modern History 



I 

J Isaeus; Isocrates. 



Irving, Washington. 



Rev. Robert Henry Charles, M.A., D.D., D.Litt. c 

Grinfield Lecturer, and Lecturer in Biblical Studies, Oxford. Fellow of the British 
Academy. Formerly Professor of Biblical Greek, Trinity College, Dublin. Author"! Isaiah, Ascension of. 

of Critical History of the Doctrine of a Future Life; Book of Jubilees; &c. ! 

Richard Lydekker, F.R.S., F.Z.S., F.G.S. , 

Member of the Staff of the Geological Survey of India 1 874-1 882. Author of Cata- Hyracoidea; 
logues of Fossil Mammals, Reptiles and Birds in the British Museum; The Deer of \ Ibex {in part); 
all Lands; &c. [ Indri; Insectivora. 

R. Phene Spiers. F.S.A., F.R.I.B.A. 

Formerly Master of the Architectural School, Royal Academy, London. Past 
President of Architectural Association. Associate and Fellow of King's College, 
London. Corresponding Member of the Institute of France. Editor of Fergusson's 
History of Architecture. Author of Architecture; East and West; &c. 



Hypaethros. 



INITIALS AND HEADINGS OF ARTICLES 



XJ 



R. S. C. 

s. 

R. Tr. 
S. A. C. 



Robert Seymour Conway, M.A., D.Litt. (Cantab.). [ 

Professor of Latin and Indo-European Philology in the University of Manchester. J 
Formerly Professor of Latin in University College, Cardiff; and Fellow of Gonville 
and Caius College, Cambridge. Author of The Italic Dialects. *■ 

The Right Hon. the Earl of Selborne. J" 

See the biographical article, Selborne, ist Earl of. \ 



Iguvium; Iovilae. 



Hymns. 



Roland Truslove, M.A. 

Formerly Scholar of Christ Church, Oxford. 
at Worcester College, Oxford. 



flndo-China, French 

Dean, Fellow and Lecturer in Classics -\ /■ ■hart) 



Ishmael. 



s. 


Bl. 


T. 


As. 


T. 


A.I 


T 


Ba. 



-j Iceland: 



T. F. 

T. F. C. 
T. H. H.* 

T. K. C. 
Th. T. 

W. A. B. C. 

W. A. P. 
W. C. U. 

W. F. C. 
W. F. Sh. 
W. G. 

W.Go. 

W. H. F. 
W. H. Po. 



Stanley Arthur Cook, M.A. 

Lecturer in Hebrew and Syriac, and formerly Fellow, Gonville and Caius College, 
Cambridge. Editor for Palestine Exploration Fund. Author of Glossary of Aramaic 
Inscriptions; The. Laws of Moses and the Code of Hammurabi; Critical Notes on Old 
Testament History; Religion of Ancient Palestine; &c. 

Sigfus Blondal. 

Librarian of the University of Copenhagen. 

Thomas Ashby, M.A., D.Litt. (Oxon.). 

Director of British School of Archaeology at Rome. Formerly Scholar of Christ. 
Church, Oxford. Craven Fellow, 1897. Conington Prizeman, 1906. Member 
of the Imperial German Archaeological Institute. 

Thomas Allan Ingram, M.A., LL.D. 
Trinity College, Dublin. 

Sir Thomas Barclay, M.P. 

Member of the Institute of International Law. Member of the Supreme Council 
of the Congo Free State. Officer of the Legion of Honour. Author of Problems 
of International Practice and Diplomacy; &c. M.P. for Blackburn, 1910. 

Rev. Thomas Fowler, M.A., D.D., LL.D. (1832-1004). 

President of Corpus Christi College, Oxford, 1881-1904. Honorary Fellow of 
Lincoln College. Professor of Logic, 1873-1888. Vice-Chancellor of the University 
of Oxford, 1899-1901. Author of Elements of Deductive Logic; Elements of Inductive 
Logic; Locke ("English Men of Letters "); Shaftesbury and Hutcheson (" English 
Philosophers "); &c. 

Theodore Freylinghuysen Collier, Ph.D. 

Assistant Professor of History, Williams College, Williamstown, Mass., U.S.A. 

Colonel Sir Thomas Hungerford Holdich, K.C.M.G., K.C.I.E., Hon.D.Sc. f 

Superintendent, Frontier Surveys, India^ 1892-1898^ Gold Medallist, R.G.S., J r n( j us 



Recent Literature, 



Interamna Lirenas; Ischia 

f Illegitimacy; 

\ Insurance (in par') 



Immunity. 
International Law. 



Hutcheson, Francis 

(in part). 



Innocent IX.-XII1. 



Author of The Indian Borderland; The Countries of the King's', 
Tibet; &c. I 



London, 1887 
Award; India; 

Rev. Thomas Kelly Cheyne, D.D. 

See the biographical article, Cheyne, T. K 

Thorvaldur Thoroddsen. 



Icelandic Expert and Explorer. Honorary Professor in the University of Copenhagen. 
Author of History of Icelandic Geography; Geological Map of Iceland; &c. 



J Isaiah. 

j Iceland: Geography and 

j Statistics. 



Hyeres; Innsbruck; 
Interlaken; Iseo, Lake of 
Isere (River); 
Isere (Department). 



Hydraulics. 



Rev. William Augustus Brevoort Coolidge, M.A., F.R.G.S., Ph.D. (Bern). 

Fellow of Magdalen College, Oxford. Professor of English History, St David's 
College, Lampeter, 1 880-1 881. Author of Guide du Haut Dauphine; The Range 
of the Todi; Guide to Grindelwald; Guide to Switzerland; The Alps in Nature and in 
History; &c. Editor of The Alpine Journal, 1880-1881 ; &c. 

Walter Alison Phillips, M.A. r 

Formerly Exhibitioner of Merton College and Senior Scholar of St John's College, J Innocent III. IV. 
Oxford. Author of Modern Europe; &c. j "' 

William Cawthorne Unwin, LL.D., F.R.S., M.Inst.CE., M.Inst.M.E r 
A.R.I. B. A. 

Emeritus Professor, Central Technical College, City and Guilds of London Institute. 
Author of Wrought Iron Bridges and Roofs; Treatise on Hydraulics; &c. I 

William Feilden Craies, M.A. 1" 

B.irristei'-at-Law, Inner Temple. Lecturer on Criminal Law, King's College,-^ Indictment. 
London. Editor of Archbold's Criminal Pleading (23rd edition). [ 

William Fleetwood Sheppard, M.A. r 

Senior Examiner in the Board of Education, London. Formerly Fellow of Trinity \ Interpolation. 
College, Cambridge. Senior Wrangler, 1884. [ 

William Garxt.tt, M.A., D.C.L. r 

Educational Adviser to the London County Council. Formerly Fellow and Lecturer J n j f 

of St John's College, Cambridge. Principal and Professor of Mathematics, Durham 1 H y arometer ' 
College of Science, Newcastle-on-Tyne. Author of Elementary Dynamics ; &c. I 

William Gow, M.A., Ph.D. r 

Secretary of the British and Foreign Marine Insurance Co. Ltd., Liverpool. Lecturer J Insurance* Marine 
on Marine 1 nsurance at University College, Liverpool. Author of Marine Insurance ■ \ 
&c. ' I 



Sir William Henry Flower, F.R.S. 

See the biographical article, Flower, Sir W. H. 

W. Haldaxe Porter. 

Barrister-at-Law, Middle Temple. 



-j Ibex (in part). 

j Ireland: Statistics and 
\ Administration. 



W. Ma. 
W. McD. 

W. M. L. 

W. M. Ra. 
W. P.. So. 

W. T. T.-D, 



W.Wn. 
W. W H. 



INITIALS AND HEADINGS OF ARTICLES 



Sir William Markby, K.C.I.E. 

See the biographical article, Markby, Sir William. 



■{ Indian Law. 



William McDougall, M.A. 

Wilde Reader in Mental Philosophy in the University of Oxford. Formerly Fellow ■< Hypnotism. 
of St John's College, Cambridge. ' 

Wallace Martin Lindsay, M.A., Litt.D., LL.D. f 

Professor of Humanity, University of St Andrews. Fellow of the British Academy. J »__ ._*. . r .. /. _,. 

Formerly Fellow of Jesus College, Oxford. Author of Handbook of Latin Inscrip- 1 inscriptions, Latin (til pari). 

tions ; The Latin Language ; &c. I 

Sir William Mitchell RamSay, Litt.D., D.C.L. J. 

See the biographical article, Ramsay, Sir W. Mitchell. |_ lconiun *. 

William Ritchie Sorley, M.A., Litt.D., LL.D. ^ r 

Professor of Moral Philosophy in the University" of Cambridge. Fellow of King's J T ... . 

College, Cambridge. Fellow of the British Academy. Formerly Fellow of Trinity 1 * a mollCmlS. 

College. Author of The Ethics of Naturalism; The Interpretation of Evolution; &c. L 
Sir William Turner Thiselton-Dyer, F.R.S., K.C.M.G., CLE., D.Sc, LL.D 
Ph.D., F.L.S. 

Hon. Student of Christ Church, Oxford. Director, Royal Botanic Gardens, Kew, . 

1885-1905. Botanical Adviser to Secretary of State for Colonies, 1902-1906. 

Joint-author of Flora of Middlesex. Editor of Flora Capenses and Flora of Tropical 

Africa. 

William Watson, D.Sc, F.R.S., A.R.C.S. 

Assistant Professor of Physics, Royal College of Science, London. Vice-President 
of the Physical Society. Author of A Text Book of Practical Physics; &c. 

Sir William Wilson Hunter. 

See the biographical article, Hunter, Sir William Wilson. 



Huxley. 



Inclinometer. 



J 

L 

f India: History {in part); 
■y Geography and Statistics 
[ {in part). 



PRINCIPAL UNSIGNED ARTICLES 




Husband and Wife. 


Illinois. 


Infant. 


Intestacy. 


Hyacinth. 


Illumination. 


Infanticide. 


Inverness-shire 


Hyderabad. 


Illyria. 


Infinite. 


Investiture. 


Hydrogen. 


Image. 


Influenza. 


Iodine. 


Hydropathy. 


Impeachment. 


Inheritance. 


Iowa. 


Hydrophobia. 


Income Tax. 


Injunction. 


Ipecacuanha. 


Ice. 


Indiana. 


Ink. 


Iris. 


Ice- Yachting. 


Indian Mutiny. 


Inkerman. 


Iron. 


Idaho. 


Indicator. 


International, The. 


Irrigation. 


Iguana. 









ENCYCLOPEDIA BRITANNICA 



ELEVENTH EDITION 



VOLUME XIV 



HUSBAND, properly the " head of a household," but now 
chiefly used in the sense of a man legally joined by marriage to 
a woman, his "wife"; the legal relations between them are 
treated below under Husband and Wife. The word appears 
in O. Eng. as husbonda, answering to the Old Norwegian 
husbondi, and means the owner or freeholder of a hus, or house. 
The last part of the word still survives in " bondage " and " bond- 
man," and is derived from bua, to dwell, which, like Lat. colere, 
means also to till or cultivate, and to have a household. " Wife," 
in O. Eng. wif, appears in all Teutonic languages except Gothic; 
cf. Ger. Weib, Dutch wijf, &c, and meant originally simply 
a female, " woman " itself being derived from wijman, the 
pronunciation of the plural wimmen still preserving the original i. 
Many derivations of " wife " have been given; thus it has been 
connected with the root of " weave," with the Gothic waibjan, 
to fold or wrap up* referring to the entangling clothes worn 
by a woman, and also with the root of vibrare, to tremble. 
These are all merely guesses, and the ultimate history of the 
word is lost. It does not appear outside Teutonic languages. 
Parallel to " husband " is " housewife," the woman managing 
a household. The earlier kuswif was pronounced hussif, and 
this pronunciation survives in the application of the word to 
a small case containing scissors, needles and pins, cottons, &c. 
From this form also derives " hussy," now only used in a de- 
preciatory sense of a light, impertinent girl. Beyond the meaning 
of a husband as a married man, the word appears in connexion 
with agriculture, in " husbandry "and " husbandman." Accord- 
ing to some authorities " husbandman " meant originally in 
the north of England a holder of a " husbandland," a manorial 
tenant who held two ox-gangs or virgates, and ranked next 
below the yeoman (see J. C. Atkinson in Notes and Queries, 
6th series, vol. xii., and E. Bateson, History of Northumberland, 
ii., 1893). From the idea of the manager of a household, 
" husband " was in use transferred to the manager of an estate, 
and the title was held by certain officials, especially in the great 
trading companies. Thus the " husband " of the East India 
Company looked after the interests of the company at the 
custom-house. The word in this sense is practically obsolete, 
but it still appears in " ship's husband," an agent of the owners 
of a ship who looks to the proper equipping of the vessel, and her 
repairs, procures and adjusts freights, keeps the accounts, makes 



charter-parties and acts generally as manager of the ship's 
employment. Where such an agent is himself one of the owners 
of the vessel, the name of " managing owner " is used. The 
" ship's husband " or " managing owner " must register his 
name and address at the port of registry (Merchant Shipping 
Act 1894, § 59). From the use of " husband " for a good and 
thrifty manager of a household, the verb " to husband " means 
to economize, to lay up a store, to save. 

HUSBAND AND WIFE, Law relating to. For the modes 
in which the relation of husband and wife may be constituted 
and dissolved, see Marriage and Divorce. The present article 
will deal only with the effect of marriage on the legal position 
of the spouses. The person chiefly affected is the wife, who 
probably in all political systems becomes subject, in consequence 
of marriage, to some kind of disability. The most favourable 
system scarcely leaves her as free as an unmarried woman; and 
the most unfavourable subjects her absolutely to the authority 
of her husband. In modern times the effect of marriage on 
property is perhaps the most important of its consequences, 
and on this point the laws of different states show wide diversity 
of principles. 

The history of Roman law exhibits a transition from an 
extreme theory to its opposite. The position of the wife in the 
earliest Roman household was regulated by the law of Manus. 
She fell under the " hand " of her husband, — became one of his 
family, along with his sons and daughters, natural or adopted, 
and his slaves. The dominion which, so far as the children 
was concerned, was known as the patria potestas, was, with 
reference to the wife, called the manus. The subject members 
of the family, whether wife or children, had, broadly speaking, 
no rights of their own. If this institution implied the complete 
subjection of the wife to the husband, it also implied a much 
closer bond of union between them than we find in the later 
Roman law. The wife on her husband's death succeeded, like 
the children, to freedom and a share of the inheritance. Manus, 
however, was not essential to a legal marriage; its restraints 
were irksome and unpopular, and in course of time it ceased 
to exist, leaving no equivalent protection of the stability of 
family life. The later Roman marriage left the spouses com- 
paratively independent of each other. The distance between 
the two modes of marriage may be estimated by the fact that, 



HUSBAND AND WIFE 



while under the former the wife was one of the husband's immediate 
heirs, under the latter she was called to the inheritance only 
after his kith and kin had been exhausted, and only in preference 
to the treasury. It seems doubtful how far she had, during 
the continuance of marriage, a legal right to enforce aliment 
from her husband, although if he neglected her she had the 
unsatisfactory remedy of an easy divorce. The law, in fact, pre- 
ferred to leave the parties to arrange their mutual rights and 
obligations by private contracts. Hence the importance of the law 
of settlements {Dotes) . The Dos and the Donatio ante nuptias were 
settlements by or on behalf of the husband or wife, during the 
continuance of the marriage, and the law seems to have looked 
with some jealousy on gifts made by one to the other in any 
less formal way, as possibly tainted with undue influence. During 
the marriage the husband had the administration of the property. 
The manus of the Roman law appears to be only one instance 
of an institution common to all primitive societies. On the 
continent of Europe after many centuries, during which local 
usages were brought under the influence of principles derived 
from the Roman law, a theory of marriage became established, 
the leading feature of which is the community of goods between 
husband and wife. Describing the principle as it prevails in 
France, Story {Conflict of Laws, § 130) says: " This community 
or nuptial partnership (in the absence of any special contract) 
generally extends to all the movable property of the husband 
and wife, and to the fruits, income and revenue thereof. . . . 
It extends also to all immovable property of the husband and 
wife acquired during the marriage, but not to such immovable 
property as either possessed at the time of the marriage, or 
which came to them afterwards by title of succession or by gift. 
The property thus acquired by this nuptial partnership is liable 
to the debts of the parties existing at the time of the marriage; 
to the debts contracted by the husband during the community, 
or by the wife during the community with the consent of the 
husband; and to debts contracted for the maintenance of the 
family. . . . The husband alone is entitled to administer the 
property of the community, and he may alien, sell or mortgage 
it without the concurrence of the wife." But he cannot dispose 
by will of more than his share of the common property, nor can 
he part with it gratuitously inter vivos. The community is 
dissolved by death (natural or civil), divorce, separation of 
body or separation of property. On separation of body or of 
property the wife is entitled to the full control of her movable 
property, but cannot alien her immovable property, without 
her husband's consent or legal authority. On the death of 
either party the property is divided in equal moieties between 
the survivor and the heirs of the deceased. 

Law of England. — The English common law as usual followed 

its own course in dealing with this subject, and in no department 

were its rules more entirely insular and independent. The 

text writers all assumed two fundamental principles, which 

between them established a system of rights totally unlike that 

just described. Husband and wife were said to be one person in 

the eye of the law — unica persona, quia caro una et sanguis unus. 

Hence a man could not grant or give anything to his wife, 

because she was himself, and if there were any compacts between 

them before marriage they were dissolved by the union of persons. 

Hence, too, the old rule of law, now greatly modified, that husband 

and wife could not be allowed to give evidence against each 

other, in any trial, civil or criminal. The unity, however, was 

one-sided only; it was the wife who was merged in the husband, 

not the husband in the wife. And when the theory did not 

apply, the disabilities of " coverture " suspended the active 

exercise of the wife's legal faculties. The old technical phraseology 

described husband and wife as baron and feme ; the rights of 

the husband were baronial rights. From one point of view the 

wife was merged in the husband, from another she was as one of 

his vassals. A curious example is the immunity of the wife in 

certain cases from punishment for crime committed in the 

presence and on the presumed coercion of the husband. " So 

great a favourite," says Blackstone, " is the female sex of the 

laws of England." 



The application of these principles with reference to the 
property of the wife, and her capacity to contract, may now be 
briefly traced. 

The freehold property of the wife became vested in the husband 
and herself during the coverture, and he had the management 
and the profits. If the wife had been in actual possession at 
any time during the marriage of an estate of inheritance, and if 
there had been a child of the marriage capable of inheriting, 
then the husband became entitled on his wife's death to hold 
the estate for his own life as tenant by the curtesy of England 
{curialitas) } Beyond this, however, the husband's rights did 
not extend, and the wife's heir at last succeeded to the inheritance. 
The wife could not part with her real estate without the concur- 
rence of the husband; and even so she must be examined 
apart from her husband, to ascertain whether she freely and 
voluntarily consented to the deed. 

With regard to personal property, it passed absolutely at 
common law to the husband. Specific things in the possession 
of the wife {choses in possession) became the property of the 
husband at once; things not in possession, but due and re- 
coverable from others {choses in action), might be recovered 
by the husband. A chose in action not reduced into actual 
possession, when the marriage was dissolved by death, reverted 
to the wife if she was the survivor; if the husband survived 
he could obtain possession by taking out letters of administra- 
tion. A chose in action was to be distinguished from a specific 
thing which, although the property of the wife, was for the 
time being in the hands of another. In the latter case the 
property was in the wife, and passed at once to the husband; 
in the former the wife had a mere jus in personam, which the 
husband might enforce if he chose, but which was still cap- 
able of reverting to the wife if the husband died without 
enforcing it. 

The chattels real of the wife {i.e., personal property, dependent 
on, and partaking of, the nature of realty, such as leaseholds) 
passed to the husband, subject to the wife's right of survivorship, 
unless barred by the husband by some act done during his life. 
A disposition by will did not bar the wife's interest; but any 
disposition inter vivos by the husband was valid and effective. 

The courts of equity, however, greatly modified the rules of 
the common law by the introduction of the wife's separate 
estate, i.e. property settled to the wife for her separate use, 
independently of her husband. The principle seems to have 
been originally admitted in a case of actual separation, when 
a fund was given for the maintenance of the wife while living 
apart from her husband. And the conditions under which 
separate estate might be enjoyed had taken the Court of Chancery 
many generations to develop. No particular form of words was 
necessary to create a separate estate, and the intervention of 
trustees, though common, was not necessary. A clear intention 
to deprive the husband of his common law rights was sufficient 
to do so. In such a case a married woman was entitled to deal 
with her property as if she was unmarried, although the earlier 
decisions were in favour of requiring her binding engagements 
to be in writing or under seal. But it was afterwards held that 
any engagements, clearly made with reference to the separate 
estate, would bind that estate, exactly as if the woman had been 
a feme sole. Connected with the doctrine of separate use was 
the equitable contrivance of restraint on anticipation with which 
later legislation has not interfered, whereby property might be 
so settled to the separate use of a married woman that she could 
not, during coverture, alienate it or anticipate the income. 
No such restraint is recognized in the case of a man or of a feme 
sole, and it depends entirely on the separate estate; and the 
separate estate has its existence only during coverture, so that 
a woman to whom such an estate is given may dispose of it so 
long as she is unmarried, but becomes bound by the restraint as 
soon as she is married. In yet another way the court of Chancery 
interfered to protect the interests of married women. When a 

1 Curtesy or courtesy has been explained by legal writers as 
" arising by favour of the law of England." The word has nothing 
to do with courtesy in the sense of complaisance. 



HUSBAND AND WIFE 



husband sought the aid of that court to get possession of his 
wife's choses in action, he was required to make a provision 
for her and her children out of the fund sought to be recovered. 
This is called the wife's equity to a settlement, and is said to be 
based on the original maxim of Chancery jurisprudence, that 
" he who seeks equity must do equity." Two other property 
interests of minor importance are recognised. The wife's pin- 
money is a provision for the purchase of clothes and ornaments 
suitable to her husband's station, but it is not an absolute 
gift to the separate use of the wife; and a wife surviving her 
husband cannot claim for more than one year's arrears of pin- 
money. Paraphernalia are jewels and other ornaments given 
to the wife by her husband for the purpose of being worn by her, 
but not as her separate property. The husband may dispose 
of them by act inter vivos but not by will, unless the will confers 
other benefits on the wife, in which case she must elect between 
the will and the paraphernalia. She may also on the death 
of the husband claim paraphernalia, provided all creditc rs 
have been satisfied, her right being superior to that of any 
legatee. 

The corresponding interest of the wife in the property of the 
husband is much more meagre and illusory. Besides a general 
right to maintenance at her husband's expense, she has at common 
law a right to dower (q.v.) in her husband's lands, and to a pars 
rationabilis (third) of his personal estate, if he dies intestate. 
The former, which originally was a solid provision for widows, 
has by the ingenuity of conveyancers, as well as by positive 
enactment, been reduced to very slender dimensions. It may 
be destroyed by a mere declaration to that effect on the part 
of the husband, as well as by his conveyance of the land or by 
his will. 

The common practice of regulating the rights of husband, 
wife and children by marriage settlements obviates the hardships 
of the common law — at least for the women of the wealthier 
classes. The legislature by the Married Women's Property 
Acts of 1870, 1874, 1882 (which repealed and consolidated the acts 
of 1870 and 1874), 1893 and 1907 introduced very considerable 
changes. The chief provisions of the Married Women's Property 
Act 1882, which enormously improved the position of women 
unprotected by marriage settlement, are, shortly, that a married 
woman is capable of acquiring, holding and disposing of by will 
or otherwise, any real and personal property, in the same manner 
as if she were a. feme sole, without the intervention of any trustee. 
The property of a woman married after the beginning of the 
act, whether belonging to her at the time of marriage or acquired 
after marriage, is held by her as a, feme sole. The same is the case 
with property acquired after the beginning of the act by a woman 
married before the act. After marriage a woman remains liable 
for antenuptial debts and liabilities, and as between her and her 
husband, in the absence of contract to the contrary, her separate 
property is deemed primarily liable. The husband is only 
liable to the extent of property acquired from or through his 
wife. The act also contained provisions as to stock, investment, 
insurance, evidence and other matters. The effect of the act 
was to render obsolete the law as to what created a separate 
use or a reduction into possession of choses in action, as to equity 
to a settlement, as to fraud on the husband's marital rights, 
and as to the inability of one of two married persons to give 
a gift to the other. Also, in the case of a gift to a husband and 
wife in terms which would make them joint tenants if unmarried, 
they no longer take as one person but as two. The act contained 
a. special saving of existing and future settlements; a settlement 
being still necessary where it is desired to secure only the enjoy- 
ment of the income to the wife and to provide for children. 
The act by itself would enable the wife, without regard to family 
claims, instantly to part with the whole of any property which 
might come to her. Restraint on anticipation was preserved 
by the act, subject to the liability of such property for antenuptial 
debts, and to the power given by the Conveyancing Act 1881 
to bind a married woman's interest notwithstanding a clause 
of restraint. The Married Women's Property Act of 1893 
repealed two clauses in the act of 1882, the exact bearing of 



which had been a matter of controversy. It provided specifically 
that every contract thereinafter entered into by a married 
woman, otherwise than as an agent, should be deemed to be a 
contract entered into by her with respect to and be binding 
upon her separate property, whether she was or was not in fact 
possessed of or entitled to any separate property at the time 
when she entered into such contract, that it should bind all 
separate property which she might at any time or thereafter 
be possessed of or entitled to, and that it should be enforceable 
by process of law against all property which she might thereafter, 
while discovert, be possessed of or entitled to. The act of 1907 
enabled a mprried woman, without her husband, to dispose of 
or join in disposing of, real or personal property held by her 
solely or jointly as trustee or personal representative, in like 
manner as if she were a. feme sole. It also provided that a settle- 
ment or agreement for settlement whether before or after 
marriage, respecting the property of the woman, should not 
be valid unless executed by her if she was of full age or confirmed 
by her after she attained full age. The Married Women's 
Property Act 1908 removed a curious anomaly by enacting 
that a married woman having separate property should be 
equally liable with single women and widows for the maintenance 
of parents who are in receipt of poor relief. 

The British colonies generally have adopted the principles of 
the English acts of 1882 and 1893. 

Law of Scotland. — The law of Scotland differs less from English 
law than the use of a very different terminology would lead us to 
suppose. The phrase communio bonorum has been employed to 
express the interest which the spouses have in the movable property 
of both, but its use has been severely censured as essentially in- 
accurate and misleading. It has been contended that there was no 
real community of goods, and no partnership or societas between 
the spouses. The wife's movable property, with certain exceptions, 
and subject to special agreements, became as absolutely the property 
of the husband as it did in English law. The notion of a communio 
was, however, favoured by the peculiar rights of the wife and children 
on the dissolution of the marriage. Previous to the Intestate 
Movable Succession (Scotland) Act 1855 the law stood as follows. 
The fund formed by the movable property of both spouses may be 
dealt with by the husband as he pleases during life; it is increased 
by his acquisitions and diminished by his debts. The respective 
shares contributed by husband and wife return on the dissolution of 
the marriage to them or their representatives if the marriage be 
dissolved within a year and a day, and without a living child. Other- 
wise the division is into two or three shares, according as children are 
existing or not at the dissolution of the marriage. On the death of 
the husband, his children take one-third (called legitim), the widow 
takes" one-third (jus relictae), and the remaining one-third (the dead 
part) goes according to his will or to his next of kin. If there be no 
children, the jus relictae and the dead's part are each one-half. If 
the wife die before the husband, her representatives, whether children 
or not, are creditors for the value of her share. The statute above- 
mentioned, however, enacts that " where a wife shall predecease her 
husband, the next of kin, executors or other representatives of such 
wife, whether testate or intestate, shall have no right to any share of 
the goods in communion; nor shall any legacy or bequest or testa- 
mentary disposition thereof by such wife, affect or attach to the said 
goods or any portion thereof." It also abolishes the rule by which 
the shares revert if the marriage does not subsist for a year and a day. 
Several later acts apply to Scotland some of the principles of the 
English Married Women's Property Acts. These are the Married 
Women's Property (Scotland) Act 1877, which protects the earnings, 
&c, of wives, and limits the husband's liability for antenuptial debts 
of the wife, the Married Women's Policies of Assurance (Scotland) 
Act 1880, which enables a woman to contract for a policy of assurance 
for her separate use, and the Married Women's Property (Scotland) 
Act 1 88 1, which abolished the jot mariti. 

A wife's heritable property does not pass to the husband on 
marriage, but he acquires a right to the administration and profits. 
His courtesy, as in English law, is also recognized. On the other 
hand, a widow has a terce or life-rent of a third part of the husband's 
heritable estate, unless she has accepted a conventional provision. 

Continental Europe. — Since 1882 English legislation in the matter 
of married women's property has progressed from perhaps the most 
backward to the foremost place in Europe. By a curious contrast, 
the only two European countries where, in the absence of a settle- 
ment to the contrary, independence of the wife's property was recog- 
nized, were Russia and Italy. But there is now a marked tendency 
towards contractual emancipation. Sweden adopted a law on this 
subject in 1874, Denmark in 1880, Norway in 1888. Germany 
followed, the Civil Code which came into operation in 1900 (Art, 
1367) providing that the wife's wages or earnings shall form part of 
her Vorbehaltsgut or separate property, which a previous article 



HUSHI— HUSS 



(!365) placed beyond the husband's control. As regards property 
accruing to the wife in Germany by succession, will or gift inter 
vivos, it is only separate property where the donor has deliberately 
stipulated exclusion of the husband's right. 

In France it seemed as if the system of community of property 
was ingrained in the institutions of the country. But a law of 1907 
has brought France into line with other countries. This law gives a 
married woman sole control over earnings from her personal work 
and savings therefrom. She can with such money acquire personalty 
or realty, over the former of which she has absolute control. But 
if she abuses her rights by squandering her money or administering 
her property badly or imprudently the husband may apply to the 
court to have her freedom restricted. 

American Law. — In the United States, the revolt against the 
common law theory of husband and wife was carried farther than in 
England, and legislation early tended in the direction of absolute 
equality between the sexes. Each state has, however, taken its 
own way and selected its own time for introducing modifications of 
the existing law, so that the legislation on this subject is now 
exceedingly complicated and difficult. James Schouler (Law of 
Domestic Relations) gives an account of the general result in the 
different states to which reference may be made. The peculiar 
system of Homestead Laws in many of the states (see Homestead 
and Exemption Laws) constitutes an inalienable provision for the 
wife and family of the householder. 

HUSHI (Rumanian Husi), the capital of the department 
of Falciu, Rumania; on a branch of the Jassy-Galatz railway, 
9 m. W. of the river Pruth and the Russian frontier. Pop. 
(1900) 15,404, about one-fourth being Jews. Hushi is an episcopal 
see. The cathedral was built in 1491 by Stephen the Great of 
Moldavia. There are no important manufactures, but a large 
fair is held annually in September for the sale of live-stock, 
and wine is produced in considerable quantities. Hushi is said 
to have been founded in the 15th century by a colony of Hussites, 
from whom its name is derived. The treaty of the Pruth between 
Russia and Turkey was signed here in 1711. 

HUSKISSON, WILLIAM (1770-1830), English statesman and 
financier, was descended from an old Staffordshire family of 
moderate fortune, and was born at Birch Moreton, Worcester- 
shire, on the nth of March 1770. Having been placed in his 
fourteenth year under the charge of his maternal great-uncle 
Dr Gem, physician to the English embassy at Paris, in 1783 
he passed his early years amidst a political fermentation which 
led him to take a deep interest in politics. Though he approved 
of the French Revolution, his sympathies were with the more 
moderate party, and he became a member of the " club of 1789," 
instituted to support the new form of constitutional monarchy 
in opposition to the anarchical attempts of the Jacobins. He 
early displayed his mastery of the principles of finance by a 
Di scours delivered in August 1790 before this society, in regard 
to the issue of assignats by the government. The Discours 
gained him considerable reputation, but as it failed in its purpose 
he withdrew from the society. In January 1 793 he was appointed 
by Dundas to an office created to direct the execution of the 
Aliens Act; and in the discharge of his delicate duties he mani- 
fested such ability that in 1795 he was appointed under-secretary 
at war. In the following year he entered parliament as member for 
Morpeth, but for a considerable period he took scarcely any part 
in the debates. In 1800 he inherited a fortune from Dr Gem. 
On the retirement of Pitt in 1801 he resigned office, and after 
contesting Dover unsuccessfully he withdrew for a time into 
private life. Having in 1804 been chosen to represent Liskeard, 
he was on the restoration of the Pitt ministry appointed secretary 
of the treasury, holding office till the dissolution of the ministry 
after the death of Pitt in January 1806. After being elected 
for Harwich in 1807, he accepted the same office under the duke 
of Portland, but he withdrew from the ministry along with 
Canning in 1809. In the following year he published a pamphlet 
on the currency system, which confirmed his reputation as the 
ablest financier of his time; but his free-trade principles did not 
accord with those of his party. In 1812 he was returned for 
Chichester. When in 1814 he re-entered the public service, it 
was only as chief commissioner of woods and forests, but his 
influence was from this time very great in the commercial and 
financial legislation of the country. He took a prominent part 
in the corn-law debates of 1814 and 1815; and in 1819 he 
presented a memorandum to Lord Liverpool advocating a large 



reduction in the unfunded debt, and explaining a method fot 
the resumption of cash payments, which was embodied in the 
act passed the same year. In 1821 he was a member of the 
committee appointed to inquire into the causes of the agricultural 
distress then prevailing, and the proposed relaxation of the corn 
laws embodied in the report was understood to have been chiefly 
due to his strenuous advocacy. In 1823 he was appointed 
president of the board of trade and treasurer of the navy, and 
shortly afterwards he received a seat in the cabinet. In the 
same year he was returned for Liverpool as successor to Canning, 
and as the only man who could reconcile the Tory merchants 
to a free trade policy. Among the more important legislative 
changes with which he was principally connected were a reform 
of the Navigation Acts, admitting other nations to a full equality 
and reciprocity of shipping duties; the repeal of the labour laws; 
the introduction of a new sinking fund; the reduction of the 
duties on manufactures and on the importation of foreign goods, 
and the repeal of the quarantine duties. In accordance with 
his suggestion Canning in 1827 introduced a measure on the 
corn laws proposing the adoption of a sliding scale to regulate 
the amount of duty. A misapprehension between Huskisson 
and the duke of Wellington led to the duke proposing an amend- 
ment, the success of which caused the abandonment of the 
measure by the government. After the death of Canning in the 
same year Huskisson accepted the secretaryship of the colonies 
under Lord Goderich, an office which he continued to hold in 
the new cabinet formed by the duke of Wellington in the following 
year. After succeeding with great difficulty in inducing the 
cabinet to agree to a compromise on the corn laws, Huskisson 
finally resigned office in May 1829 on account of a difference 
with his colleagues in regard to the disfranchisement of East 
Retford. On the 1 5th of September of the following year he was 
accidentally killed by a locomotive engine while present at the 
opening of the Liverpool and Manchester railway. 
See the Life of Huskisson, by J. Wright (London, 1831). 

HUSS (or Hus), JOHN (c. 1373-1415), Bohemian reformer and 
martyr, was born at Hussinecz, 1 a market village at the foot of 
the Bohmerwald, and not far from the Bavarian frontier, between 
1373 and 1375, the exact date being uncertain. His parents 
appear to have been well-to-do Czechs of the peasant class. 
Of his early life nothing is recorded except that, notwithstanding 
the early loss of his father, he obtained a good elementary 
education, first at Hussinecz, and afterwards at the neighbouring 
town of Prachaticz. At, or only a very little beyond, the 
usual age he entered the recently (1348) founded university of 
Prague, where he became bachelor of arts in 1393, bachelor 
of theology in 1394, and master of arts in 1396. In 1398 
he was chosen by the Bohemian " nation " of the university 
to an examinership for the bachelor's degree; in the 
same year he began to lecture also, and there is reason to 
believe that the philosophical writings of Wycliffe, with which 
he had been for some years acquainted, were his text-books. 
In October 1401 he was made dean of the philosophical faculty, 
and for the half-yearly period from October 1402 to April 1403 
he held the office of rector of the university. In 1402 also he 
was made rector or curate (capellarius) of the Bethlehem chapel, 
which had in 1391 been erected and endowed by some zealous 
citizens of Prague for the purpose of providing good popular 
preaching in the Bohemian tongue. This appoinment had 
a deep influence on the already vigorous religious life of Huss 
himself; and one of the effects of the earnest and independent 
study of Scripture into which it led him was a profound convictioft 
of the great value not only Of the philosophical but also of the 
theological writings of Wycliffe. 

This newly-formed sympathy with the English reformer did" 
not, in the first instance at least, involve Huss in any conscious 
opposition to the established doctrines of Catholicism, or in 
any direct conflict with the authorities of the church; and for 

1 From which the name Huss, or more properly Hus, an abbrevia- 
tion adopted by himself about 1396, is derived. Prior to that date 
he was invariably known as Johann Hussynecz, Hussinecz, Hussenicz 
or de Hussynecz. 



HUSS 



several years he continued to act in full accord with his archbishop 
(Sbynjek, or Sbynko, of Hasenburg). Thus in 1405 he, with 
other two masters, was commissioned to examine into certain 
reputed miracles at Wilsnack, near Wittenberg, which had 
caused that church to be made a resort of pilgrims from all parts 
of Europe. The result of their report was that all pilgrimage 
thither from the province of Bohemia was prohibited by the 
archbishop on pain of excommunication, while Huss, with the 
full sanction of his superior, gave to the world his first published 
writing, entitled De Omni Sanguine Christi Glorificato, in which 
he declaimed in no measured terms against forged miracles and 
ecclesiastical greed, urging Christians at the same time to desist 
from looking for sensible signs of Christ's presence, but rather 
to seek Him in His enduring word. More than once also Huss, 
together with his friend Stanislaus of Znaim, was appointed 
to be synod preacher, and in this capacity he delivered at the 
provincial councils of Bohemia many faithful admonitions. 
As early as the 28th of May r403, it is true, there had been held 
a university disputation about the new doctrines of Wycliffe, 
which had resulted in the condemnation of certain propositions 
presumed to be his; five years later (May 20, 1408) this decision 
had been refined into a declaration that these, forty-five in 
number, were not to be taught in any heretical, erroneous 
or offensive sense. But it was only slowly that the growing 
sympathy of Huss with Wycliffe unfavourably affected his 
relations with his colleagues in the priesthood. In 1408, however, 
the clergy of the city and archiepiscopal diocese of Prague laid 
before the archbishop a formal complaint against Huss, arising 
out of strong expressions with regard to clerical abuses of which 
he had made use in his public discourses; and the result was 
that, having been first deprived of his appointment as synodal 
preacher, he was, after a vain attempt to defend himself in 
writing, publicly forbidden the exercise of any priestly function 
throughout the diocese. Simultaneously with these proceedings 
in Bohemia, negotiations had been going on for the removal of 
the long-continued papal schism, and it had become apparent 
that a satisfactory solution could only be secured if, as seemed 
not impossible, the supporters of the rival popes, Benedict XIII. 
and Gregory XII., could be induced, in view of the approaching 
council of Pisa, to pledge themselves to a strict neutrality. 
With this end King Wenceslaus of Bohemia had requested the 
co-operation of the archbishop and his clergy, and also the 
support of the university, in both -instances unsuccessfully, 
although in the case of the latter the Bohemian " nation," with 
Huss at its head, had only been overborne by the votes of the 
Bavarians, Saxons and Poles. There followed an expression 
of nationalist and particularistic as opposed to ultramontane 
and also to German feeling, which undoubtedly was of supreme 
importance for the whole of the subsequent career of Huss. In 
compliance with this feeling a royal edict (January 18, 1409) 
was issued, by which, in alleged conformity with Paris usage, 
and with the original charter of the university, the Bohemian 
" nation " received three votes, while only one was allotted to 
the other three " nations " combined; whereupon all the 
foreigners, to the number of several thousands, almost im- 
mediately withdrew from Prague, an occurrence which led to 
the formation shortly afterwards of the university of Leipzig. 

It was a dangerous triumph for Huss; for his popularity 
at court and in the general community had been secured only 
at the price of clerical antipathy everywhere and of much German 
ill-will. Among the first results of the changed order of things 
were on the one hand the election of Huss (October 1400") to be 
again rector of the university, but on the other hand the appoint- 
ment by the archbishop of an inquisitor to inquire into charges 
of heretical teaching and inflammatory preaching brought 
against him. He had spoken disrespectfully of the church, it 
was said, had even hinted that Antichrist might be found to 
be in Rome, had fomented in his preaching the quarrel between 
Bohemians and Germans, and had, notwithstanding all that 
had passed, continued to speak of Wycliffe as both a pious man 
and an orthodox teacher. The direct result of this investigation 
is not known, but it is impossible to disconnect from it the 



promulgation by Pope Alexander V., on the 20th of December 
1409, of a bull which ordered the abjuration of all Wycliffite 
heresies and the surrender of all his books, while at the same 
time — a measure specially levelled at the pulpit of Bethlehem 
chapel — all preaching was prohibited except in localities which' 
had been by long usage set apart for that use. This decree, as 
soon as it was published in Prague (March 9, 1410), led to much 
popular agitation, and provoked an appeal by Huss to the 
pope's better informed judgment; the archbishop, however, 
resolutely insisted on carrying out his instructions, and in the 
following July caused to be publicly burned, in the courtyard 
of his own palace, upwards of 200 volumes of. the writings of 
Wycliffe, while he pronounced solemn sentence of excommunica- 
tion against Huss and certain of his friends, who had in the 
meantime again protested and appealed to the new pope 
(John XXIII.). Again the populace rose on behalf of their hero, 
who, in his turn, strong in the conscientious conviction that " in 
the things which pertain to salvation God is to be obeyed rather 
than man," continued uninterruptedly to preach in the Bethlehem 
chapel, and in the university began publicly to defend the so- 
called heretical treatises of Wycliffe, while from king and queen, 
nobles and burghers, a petition was sent to Rome praying that 
the condemnation and prohibition in the bull of Alexander V. 
might be quashed. Negotiations were carried on for some months, 
but in vain; in March 141 1 the ban was anew pronounced upon 
Huss as a disobedient son of the church, while the magistrates 
and councillors of Prague who had favoured him were threatened 
with a similar penalty in case of their giving him a contumacious 
support. Ultimately the whole city, which continued to harbour 
him, was laid under interdict; yet he went on preaching, and 
masses were celebrated as usual, so that at the date of Archbishop 
Sbynko's death in September 141 1, it seemed as if the efforts of 
ecclesiastical authority had resulted in absolute failure. 

The struggle, however, entered on a new phase with the 
appearance at Prague in May 141 2 of the papal emissary charged 
with the proclamation of the papal bulls by which a religious 
war was decreed against the excommunicated King Ladislaus 
of Naples, and indulgence was promised to all who should take 
part in it, on terms similar to those which had been enjoyed 
by the earlier crusaders to the Holy Land. By his bold and 
thorough-going opposition to this mode of procedure against 
Ladislaus, and still more by his doctrine that indulgence could 
never be sold without simony, and could not be lawfully granted 
by the church except on condition of genuine contrition and 
repentance, Huss at last isolated himself, not only from the 
archiepiscopal party under Albik of Unitschow, but also from 
the theological faculty of the university, and especially from 
such men as Stanislaus of Znaim and Stephen Paletz, who until 
then had been his chief supporters. A popular demonstration, 
in which the papal bulls had been paraded through the streets 
with circumstances of peculiar ignominy and finally burnt, led 
to intervention by Wenceslaus on behalf of public order; three 
young men, for having openly asserted the unlawfulness of the 
papal indulgence after silence had been enjoined, were sentenced 
to death (June 141 2); the excommunication against Huss was 
renewed, and the interdict again laid on all places which should 
give him shelter — a measure which now began to be more strictly 
regarded by the clergy, so that in the following December 
Huss had no alternative but to yield to the express wish of the 
king by temporarily withdrawing from Prague. A provincial 
synod, held at the instance of Wenceslaus in February 1413, 
broke up without having reached any practical result;" and 
a commission appointed shortly afterwards also failed to bring 
about a reconciliation between Huss and his adversaries. The 
so-called heretic meanwhile spent his time partly at Kozihradek, 
some 45 m. south of Prague, and partly at Krakowitz in 
the immediate neighbourhood of the capital, occasionally 
giving a course of open-air preaching, but finding his chief 
employment in maintaining that copious correspondence of 
which some precious fragments still are extant, and in the 
composition of the treatise, De Ecclesia, which subsequently 
furnished most of the material for the capital charges brought 



HUSS 



against him, and was formerly considered the most important of 
his works, though it is mainly a transcript of Wycliffe's work 
of the same name. 

During the year 1413 the arrangements for the meeting of 
a general council at Constance were agreed upon between 
Sigismund and Pope John XXIII. The objects originally 
contemplated had been the restoration of the unity of the church 
and its reform in head and members; but so great had become 
the prominence of Bohemian affairs that to these also a first 
place in the programme of the approaching oecumenical assembly 
required to be assigned, and for their satisfactory settlement 
the presence of Huss was necessary. His attendance was ac- 
cordingly requested, and the invitation was willingly accepted 
as giving him a long-wished-for opportunity both of publicly 
vindicating himself from charges which he felt to be grievous, 
and of loyally making confession for Christ. He set out from 
Bohemia on the 14th of October 1414, not, however, until he 
had carefully ordered all his private affairs, with a presentiment, 
which he did not conceal, that in all probability he was going 
to his death. The journey, which appears to have been under- 
taken with the usual passport, and under the protection of 
several powerful Bohemian friends (John of Chlum, Wenceslaus 
of Duba, Henry of Chlum) who accompanied him, was a very 
prosperous one; and at almost all the halting-places he was 
received with a consideration and enthusiastic sympathy which 
he had hardly expected to meet with anywhere in Germany. 
On the 3rd of November he arrived at Constance; shortly after- 
wards there was put into his hands the famous imperial " safe 
conduct," the promise of which had been one of his inducements 
to quit the comparative security he had enjoyed in Bohemia. 
This safe conduct, which had been frequently printed, stated 
that Huss should, whatever judgment might be passed on him, 
be allowed to return freely to Bohemia. This by no means 
provided for his immunity from punishment. If faith to him 
had not been broken he would have been sent back to Bohemia 
to be punished by his sovereign, the king of Bohemia. The 
treachery of King Sigismund is undeniable, and was indeed 
admitted by the king himself. The safe conduct was probably 
indeed given by him to entice Huss to Constance. On the 4th 
of December the pope appointed a commission of three bishops to 
investigate the case against the heretic, and to procure witnesses; 
to the demand of Huss that he might be permitted to employ 
an agent in his defence a favourable answer was at first given, 
but afterwards even this concession to the forms of justice was 
denied. While the commission was engaged in the prosecution 
of its enquiries, the flight of Pope John XXIII. took place on 
the 20th of March, an event which furnished a pretext for the 
removal of Huss from the Dominican convent to a more secure 
and more severe place of confinement under the charge of the 
bishop of Constance at Gottlieben on the Rhine. On the 4th 
of May the temper of the council on the doctrinal questions in 
dispute was fully revealed in its unanimous condemnation of 
Wycliffe, especially of the so-called " forty-five articles " as 
erroneous, heretical, revolutionary. It was not, however, until 
the 5th of June that the case of Huss came up for hearing; the 
meeting, which was an exceptionally full one, took place in the 
refectory of the Franciscan cloister. Autograph copies of his 
work De Ecclesia and of the controversial tracts which he had 
written against Paletz and Stanislaus of Znaim having been 
acknowledged by him, the extracted propositions on which the 
prosecution based their charge of heresy were read; but as 
soon as the accused began to enter upon his defence, he was 
assailed by violent outcries, amidst which it was impossible 
for him to be heard, so that he was compelled to bring his speech 
to an abrupt close, which he did with the calm remark: " In 
such a council as this I had expected to find more propriety, 
piety and order." It was found necessary to adjourn the 
sitting until the 7th of June, on which occasion the outward 
decencies were better observed, partly no doubt from the circum- 
stance that Sigismund was present in person. The propositions 
which had been extracted from the De Ecclesia were again brought 
up, and the relations between Wycliffe and Huss were discussed, 



the object of the prosecution being to fasten upon the latter the 
charge of having entirely adopted the doctrinal system of the 
former, including especially a denial of the doctrine of transub- 
stantiation. The accused repudiated the charge of having 
abandoned the Catholic doctrine, while expressing hearty 
admiration and respect for the memory of Wycliffe. Being 
next asRed to make an unqualified submission to the council, 
he expressed himself as unable to do so, while stating his willing- 
ness to amend his teaching wherever it had been shown to be 
false. With this the proceedings of the day were brought to 
a close. On the 8th of June the propositions extracted from 
the De Ecclesia were again taken up with some fulness of detail; 
some of these he repudiated as incorrectly given, others he 
defended; but when asked to make a general recantation he 
steadfastly declined, on the ground that to do so would be a 
dishonest admission of previous guilt. Among the propositions 
he could heartily abjure was that relating to transubstantiation ; 
among those he felt constrained unflinchingly to maintain 
was one which had given great offence, to the effect that Christ, 
not Peter, is the head of the church to whom ultimate appeal 
must be made. The council, however, showed itself inaccessible 
to all his arguments and explanations, and its final resolution, 
as announced by Pierre d'Ailly, was threefold: first, that 
Huss should humbly declare that he had erred in all the articles 
cited against him; secondly, that he should promise on oath 
neither to hold nor teach them in the future; thirdly, that 
he should publicly recant them. On his declining to make 
this submission he was removed from the bar. Sigismund 
himself gave it as his opinion that it had been clearly proved 
by many witnesses that the accused had taught many pernicious 
heresies, and that even should he recant he ought never to be 
allowed to preach or teach again or to return to Bohemia, but 
that should he refuse recantation there was no remedy but the 
stake. During the next four weeks no effort was spared to 
shake the determination of Huss; but he steadfastly refused 
to swerve from the path which conscience had once made clear. 
" I write this," says he, in a letter to his friends at Prague, " in 
prison and in chains, expecting to-morrow to receive sentence 
of death, full of hope in God that I shall not swerve from the 
truth, nor abjure errors imputed to me by false witnesses." 
The sentence he expected was pronounced on the 6th of July 
in the presence of Sigismund and a full sitting of the council; 
once and again he attempted to remonstrate, but in vain, and 
finally he betook himself to silent prayer. After he had under- 
gone the ceremony of degradation with all the childish formalities 
usual on such occasions, his soul was formally consigned by aE 
those present to the devil, while he himself with clasped hands 
and uplifted eyes reverently committed it to Christ. He was 
then handed over to the secular arm, and immediately led to the 
place of execution, the council meanwhile proceeding uncon- 
cernedly with the rest of its business for the day. Many 
incidents recorded in the histories make manifest the meek- 
ness, fortitude and even cheerfulness with which he went to 
his death. After he had been tied to the stake and the faggots 
had been piled, he was for the last time urged to recant, but 
his only reply was: " God is my witness that I have never 
taught or preached that which false witnesses have testified 
against me. He knows that the great object of all my preaching 
and writing was to convert men from sin. In the truth of that 
gospel which hitherto I have written, taught and preached, 
I now joyfully die." The fire was then kindled, and his voice 
as it audibly prayed in the words of the " Kyrie Eleison " was 
soon stifled in the smoke. When the flames had done their 
office, the ashes that were left and even the soil on which they 
lay were carefully removed and thrown into the Rhine. 

Not many words are needed to convey a tolerably adequate 
estimate of the character and work of the " pale thin man in 
mean attire," who in sickness and poverty thus completed the 
forty-sixth year of a busy life at the stake. The value of Huss 
as a scholar was formerly underrated. The publication of his 
Super IV. Sententiarum has proved that he was a man of profound 
learning. Yet his principal glory will always be founded on his 



HUSSAR— HUSSITES 



spiritual teaching. It might not be easy to formulate precisely 
the doctrines for which he died, and certainly some of them, 
as, for example, that regarding the church, were such as many 
Protestants even would regard as unguarded and difficult to 
harmonize with the maintenance of external church order; 
but his is undoubtedly the honour of having been the chief inter- 
mediary in handing on from Wycliffe to Luther the torch which 
kindled the Reformation, and of having been one of the bravest oi 
the martyrs who have died in the cause of honesty and freedom, 
of progress and of growth towards the light. (J. S. Bl.) 

The works of Huss are usually classed under four heads: the 
dogmatical and polemical, the homiletical, the exegetical and the 
epistolary. In the earlier editions of his works sufficient care was 
not taken to distinguish between his own writings and those of 
Wycliffe and others who were associated with him. In connexion 
with his sermons it is worthy of note that by means of them and by 
his public teaching generally Huss exercised a considerable influence 
not only on the religious life of his time, but on the literary develop- 
ment of his native tongue. The earliest collected edition of his 
works, Historia et monumenta Joannis Hus et Hieronymi Pragensis, 
was published at Nuremberg in 1558 and was reprinted with a con- 
siderable quantity of new matter at Frankfort in 1715. A Bohemian 
edition of the works has been edited by K. J. Erben (Prague, 1865- 
1868), and the Documenta J. Hus vitain, doctrinam, causam in 
Constantiensi concilio (1869), edited by F. Palacky, is very valuable. 
More recently Joannis Hus. Opera omnia have been edited by W. 
Flojshaus (Prague, 1904 fob). The De Ecclesia was published by 
Ulnch von Hutten in 1520; other controversial writings by Otto 
Brumfels in 1524; and Luther wrote an interesting preface to 
Epistolae Quaedam, which were published in 1537. These Epistolae 
have been translated into French by E. de Bonnechose (1846), and 
the letters written during his imprisonment have been edited by 
C. von Kugelgen (Leipzig, 1902). 

The best and most easily accessible information for the English 
reader on Huss is found in J. A. W. Neander's Allgemeine Geschichte 
der chrisllichen Religion und Kirche, translated by J. Torrey (1850- 
1858) ; in G. von Lechler's Wiclif und die V or geschichte der Reforma- 
tion, translated by P. Lorimer (1878); in H. H. Milman's History of 
Latin Christianity, vol. viii. (1867) ; and in M. Creighton's History of 
the Papacy (1897). Among the earlier authorities is the Historia 
Bohemica of Aeneas Sylvius (1475). The Acta of the council of 
Constance (published by P. Labbe in his Concilia, vol. xvi., 1731 ; by 
H. von der Haardt in his Magnum Constantiense concilium, vol. vi., 
1700; and by H. Finke in his Acta concilii Constantiensis, 1896); 
and J. Lenfant's Histoire de la guerre des Hussites (1731) and the same 
writer's Histoire du concile de Constance (1714) should be consulted. 
F. Palacky's Geschichte Bohmens (1864-1867) is also very useful. 
Monographs on Huss are very numerous. Among them may be 
mentioned J. A. von Helfert, Studien ilber Hus und Hieronymus 
(1853; this work is ultramontane in its sympathies) ; C. von Hofier, 
H us und der A bzug der deutsclien Professoren und Studenten aus Prag 
(1864); YV. Berger, Johannes Hus und Kbnig Sigmund (1871); 
E. Denis, Huss et la guerre des Hussites (1878); P. Uhlmann, Konig 
Sigmunds Geleit fur Hus (1894); J. Loserth, Hus und Wiclif (1884), 
translated into English by M. J. Evans (1884); A. Jeep, Gerson, 
Wiclefus, Hussus, inter se comparati (1857); and G. von Lechler, 
Johannes Hus (1889). See also Count Liitzow, The Life and Times of 
John Hus (London, 1909). 

HUSSAR, originally the name of a soldier belonging to a 
corps of light horse raised by Matthias Corvinus, king of Hungary, 
in 1458, to fight against the Turks. The Magyar huszar, from 
which the word is derived, was formerly connected with the 
Magyar husz, twenty, and was explained by a supposed raising 
of the troops by the taking of each twentieth man. According 
to the New English Dictionary the word is an adaptation of 
the Italian corsaro, corsair, a robber, and is found in 15th-century 
documents coupled with praedones. The hussar was the typical 
Hungarian cavalry soldier, and, in the absence of good light 
cavalry in the regular armies of central and western Europe, 
the name and character of the hussars gradually spread into 
Prussia, France, &c. Frederick the Great sent Major H. J. von 
Zieten to study the work of this type of cavalry in the Austrian 
service, and Zieten so far improved on the Austrian model that 
he defeated his old teacher, General Baranyai, in an encounter 
between the Prussian and Austrian hussars at Rothschloss in 
1 741. The typical uniform of the Hungarian hussar was followed 
with modifications in other European armies. It consisted of 
a busby or a high cylindrical cloth cap, jacket with heavy 
braiding, and a dolman or pelisse, a loose coat worn hanging 
from the left shoulder. The hussar regiments of the British 
army were converted from light dragoons at the following dates: 



7th (1805), 10th and 15th (1806), 18th (1807, and again on 
revival after disbandment, 1858), 8th (1822), nth (1840), 20th 
(late 2nd Bengal European Cavalry) (i860), 13th, 14th, and 19th 
(late 1st Bengal European Cavalry) (1861). The 21st Lancers 
were hussars from 1862 to 1897. 

HUSSITES, the name given to the followers of John Huss 
(1369-1415), the Bohemian reformer. They were at first often 
called Wycliffites, as the theological theories of Huss were largely 
founded on the teachings of Wycliffe. Huss indeed laid more 
stress on church reform than on theological controversy. On 
such matters he always writes as a disciple of Wycliffe. The 
Hussite movement may be said to have sprung from three 
sources, which are however closely connected. Bohemia, which 
had first received Christianity from the East, was from geo- 
graphical and other causes long but very loosely connected 
with the Church of Rome. The connexion became closer at the 
time when the schism with its violent controversies between 
the rival pontiffs, waged with the coarse invective customary 
to medieval theologians, had brought great discredit on the 
papacy. The terrible rapacity of its representatives in Bohemia, 
which increased in proportion as it became more difficult to 
obtain money from western countries such as England and France, 
caused general indignation; and this was still further intensified 
by the gross immorality of the Roman priests. The Hussite 
movement was also a democratic one, an uprising of the peasantry 
against the landowners at a period when a third of the soil 
belonged to the clergy. Finally national enthusiasm for the 
Slavic race contributed largely to its importance. The towns, 
in most cases creations of the rulers of Bohemia who had called 
in German immigrants, were, with the exception of the " new 
town " of Prague, mainly German; and in consequence of the 
regulations of the university, Germans also held almost all the 
more important ecclesiastical offices — a condition of things 
greatly resented by the natives of Bohemia, which at this period 
had reached a high degree of intellectual development. 

The Hussite movement assumed a revolutionary character 
as soon as the news of the death of Huss reached Prague. The 
knights and nobles of Bohemia and Moravia, who were in favour 
of church reform, sent to the council at Constance (September 
2nd, 141 5) a protest, known as the " protestatio Bohemorum " 
which condemned the execution of Huss in the strongest language. 
The attitude of Sigismund, king of the Romans, who sent 
threatening letters to Bohemia declaring that he would shortly 
" drown all Wycliffites and Hussites," greatly incensed the 
people. Troubles broke out in various parts of Bohemia, and 
many Romanist priests were driven from their parishes. Almost 
from the first the Hussites were divided into two sections, though 
many minor divisions also arose among them. Shortly before 
his death Huss had accepted a doctrine preached during his 
absence by his adherents at Prague, namely that of " utraquism," 
i.e. the obligation of the faithful to receive communion in both 
kinds (sub ulraque specie). This doctrine became the watchword 
of the moderate Hussites who were known as the Utraquists 
or Calixtines (caiix, the chalice), in Bohemian, podoboji ; while 
the more advanced Hussites were soon known as the Taborites, 
from the city of Tabor that became their centre. 

Under the influence of his brother Sigismund, king of the 
Romans, King Wenceslaus endeavoured to stem the Hussite 
movement. A certain number of Hussites lead by Nicolas of 
Hus — no relation of John Huss — left Prague. They held meetings 
in various parts of Bohemia, particularly at Usti, near the spot 
where the town of Tabor was founded soon afterwards. "At 
these meetings Sigismund was violently denounced, and the people 
everywhere prepared for war. In spite of the departure of many 
prominent Hussites the troubles at Prague continued. On 
the 30th of July 1419, when a Hussite procession headed by the 
priest John of Zelivo (in Ger. Selau) marched through the streets 
of Prague, stones were thrown at the Hussites from the windows 
of the town-hall of the " new town." The people, headed by 
John 2izka (1376-1424), threw the burgomaster and several 
town-councillors, who were the instigators of this outrage, 
from the windows and they were immediately killed by the 



8 



HUSSITES 



crowd. On hearing this news King Wenceslaus was seized with 
an apoplectic fit, and died a few days afterwards. The death of 
the king resulted in renewed troubles in Prague and in almost 
all parts of Bohemia. Many Romanists, mostly Germans — for 
they had almost all remained faithful to the papal cause — were 
expelled from the Bohemian cities. In Prague, in November 
14 1 9, severe fighting took place between the Hussites and the 
mercenaries whom Queen Sophia (widow of Wenceslaus and 
regent after the death of her husband) had hurriedly collected. 
After a considerable part of the city had been destroyed a truce 
was concluded on the 13th of November. The nobles, who 
though favourable to the Hussite cause yet supported the 
regent, promised to act as mediators with Sigismund; while 
the citizens of Prague consented to restore to the royal forces 
the castle of Vysehrad, which had fallen into their hands. Zizka, 
who disapproved of this compromise, left Prague and retired 
to Plzen (Pilsen). Unable to maintain himself there he marched 
to southern Bohemia, and after defeating the Romanists at 
Sudomef — the first pitched battle of the Hussite wars — he 
arrived at Usti, one of the earliest meeting-places of the Hussites. 
Not considering its situation sufficiently strong, he moved to 
the neighbouring new settlement of the Hussites, to which the 
biblical name of Tabor was given. Tabor soon became the 
centre of the advanced Hussites, who differed from the Utraquists 
by recognizing only two sacraments — Baptism and Communion — 
and by rejecting most of the ceremonial of the Roman Church. 
The ecclesiastical organization of Tabor had a somewhat puritanic 
character, and the government was established on a thoroughly 
democratic basis. Four captains of the people (hejtmane) were 
elected, one of whom was Zizka; and a very strictly military 
discipline was instituted. 

Sigismund, king of the Romans, had, by the death of his 
brother Wenceslaus without issue, acquired a claim on the 
Bohemian crown; though it was then, and remained till much 
later, doubtful whether Bohemia was an hereditary or an elective 
monarchy. A firm adherent of the Church of Rome, Sigismund 
was successful in obtaining aid from the pope. Martin V. 
issued a bull on the 17th of March 1420 which proclaimed a 
crusade " for the destruction of the WyclifBtes, Hussites and all 
other heretics in Bohemia." The vast army of crusaders, with 
which were Sigismund and many German princes, and which 
consisted of adventurers attracted by the hope of pillage from 
all parts of Europe, arrived before Prague on the 30th of June 
and immediately began the siege of the city, which had, however, 
soon to be abandoned (see Zizka, John). Negotiations took 
place for a settlement of the religious differences. The united 
Hussites formulated their demands in a statement known as 
the " articles of Prague." This document, the most important 
of the Hussite period, runs thus in the wording of the con- 
temporary chronicler, Laurence of Brezova: — 

I. The word of God shall be preached and made known in the 
kingdom of Bohemia freely and in an orderly manner by the priests 
of the Lord. . . . 

II. The sacrament of the most Holy Eucharist shall be freely 
administered in the two kinds, that is bread and wine, to all the 
faithful in Christ who are not precluded by mortal sin — according 
to the word and disposition of Our Saviour. 

III. The secular power over riches and worldly goods which the 
clergy possesses in contradiction to Christ's precept, to the prejudice 
of its office and to the detriment of the secular arm, shall be taken 
and withdrawn from it, and the clergy itself shall be brought back to 
the evangelical rule and an apostolic life such as that which Christ 
and his apostles led. . . . 

IV. All mortal sins, and in particular all public and other dis- 
orders, which are contrary to God's law. shall in every rank of life 
be duly and judiciously prohibited and destroyed by those whose 
office it is. 

These articles, which contain the essence of the Hussite doctrine, 
were rejected by Sigismund, mainly through the influence 
of the papal legates, who considered them prejudicial to the 
authority of the Roman see. Hostilities therefore continued. 
Though Sigismund had retired from Prague, the castles of 
Vysehrad and Hradcany remained in possession of his troops. 
The citizens of Prague laid siege to the Vysehrad, and towards 



the end of October (1420) the garrison was on the point of 
capitulating through famine. Sigismund attempted to relieve 
the fortress, but was decisively defeated by the Hussites on 
the 1st of November near the village of Pankrac. The castles 
of Vysehrad and Hradcany now capitulated, and shortly after- 
wards almost all Bohemia fell into the hands of the Hussites. 
Internal troubles prevented them from availing themselves 
completely of their victory. At Prague a demagogue, the 
priest John of Zelivo, for a time obtained almost unlimited 
authority over the lower classes of the townsmen; and at 
Tabor a communistic movement (that of the so-called Adamites) 
was sternly suppressed by Zizka. Shortly afterwards a new 
crusade against the Hussites was undertaken. A large German 
army entered Bohemia, and in August 142 1 laid siege to the 
town of Zatec (Saaz). The crusaders hoped to be joined in 
Bohemia by King Sigismund, but that prince was detained 
in Hungary. After an unsuccessful attempt to storm Zatec 
the crusaders retreated somewhat ingloriously, on hearing 
that the Hussite troops were approaching. Sigismund only 
arrived in Bohemia at the end of the year 142 1. He took 
possession of the town of Kutna Hora (Kuttenberg), but was 
decisively defeated by Zizka at Nemecky Brod (Deutschbrod) 
on the 6th of January 1422. Bohemia was now again for a 
time free from foreign intervention, but internal discord again 
broke out caused partly by theological strife, partly by the 
ambition of agitators. John of Zelivo was on the 9th of March 
1422 arrested by the town council of Prague and decapitated. 
There were troubles at Tabor also, where a more advanced 
party opposed Zizka's authority. Bohemia obtained a temporary 
respite when, in 1422, Prince Sigismund Korybutovic of Poland 
became for a short time ruler of the country. His authority 
was recognized by the Utraquist nobles, the citizens of Prague, 
and the more moderate Taborites, including Zizka. Korybutovic, 
however, remained but a short time in Bohemia; after his 
departure civil war broke out, the Taborites opposing in arms 
the more moderate Utraquists, who at this period are also 
called by the chroniclers the " Praguers," as Prague was their 
principal stronghold. On the 27th of April 1423, Zizka now 
again leading, the Taborites defeated at Horic the Utraquist 
army under Cenek of Wartemberg; shortly afterwards an 
armistice was concluded at Konopist. 

Papal influence had meanwhile succeeded in calling forth 
a new crusade against Bohemia, but it resulted in complete failure. 
In spite of the endeavours of their rulers, the Slavs of Poland 
and Lithuania did not wish to attack the kindred Bohemians; 
the Germans were prevented by internal discord from taking 
joint action against the Hussites; and the king of Denmark, 
who had landed in Germany with a large force intending to 
take part in the crusade, soon returned to his own country. 
Free for a time from foreign aggression, the Hussites invaded 
Moravia, where a large part of the population favoured their 
creed; but, again paralysed by dissensions, soon returned 
to Bohemia. The city of Koniggratz (Kralove Hradec), which 
had been under Utraquist rule, espoused the doctrine of Tabor, 
and called Zizka to its aid. After several military successes 
gained by Zizka (q.v.) in 1423 and the following year, a treaty 
of peace between the Hussites was concluded on the 13 th of 
September 1424 at Liben, a village near Prague, now part of 
that city. 

In 1426 the Hussites were again attacked by foreign enemies. 
In June of that year their forces, led by Prokop the Great— 
who took the command of the Taborites shortly after Zizka's 
death in October 1424 — and Sigismund Korybutovic, who had 
returned to Bohemia, signally defeated the Germans at Aussig 
(Usti nad Labem). After this great victory, and another at 
Tachau in 1427, the Hussites repeatedly invaded Germany, 
though they made no attempt to occupy permanently any part 
of the country. 

The almost uninterrupted series of victories of the Hussites 
now rendered vain all hope of subduing them by force of arms. 
Moreover, the conspicuously democratic character of the Hussite 
movement caused the German princes, who were afraid that 



HUSTING— HUTCHESON 



such views might extend to their own countries, to desire peace. 
Many Hussites, particularly the Utraquist clergy, were also in 
favour of peace. Negotiations for this purpose were to take 
place at the oecumenical council which had been summoned to 
meet at Basel on the 3rd of March 1431. The Roman see re- 
luctantly consented to the presence of heretics at this council, 
but indignantly rejected the suggestion of the Hussites that 
members of the Greek Church, and representatives of all Christian 
creeds, should also be present. Before definitely giving its consent 
to peace negotiations, the Roman Church determined on making 
a last effort to reduce the Hussites to subjection. On the 1st 
of August 143 1 a large army of crusaders, under Frederick, 
margrave of Brandenburg, whom Cardinal Cesarini accompanied 
as papal legate, crossed the Bohemian frontier; on the 14th 
of August it reached the town of Domazlice (Tauss); but on 
the arrival of the Hussite army under Prokop the crusaders 
immediately took to flight, almost without offering resistance. 

On the 15th of October the members of the a uncil, who had 
already assembled at Basel, issued a formal invitation to the 
Hussites to take part ir4 its deliberations. Prolonged negotiations 
ensued; but finally a Hussite embassy, led oy Prokop and 
including John of Rokycan, the Taborite bishop Nicolas of 
Pelhfimov, the " English Hussite," Peter Payne and many 
others, arrived at Basel on the 4th of January 1433. It was 
found impossible to arrive at an agreement. Negotiations 
were not, however, broken off; and a change in the political 
situation of Bohemia finally resulted in a settlement. In 1434 
war again broke out between the Utraquists and the Taborites. 
On the 30th of May of that year the Taborite army, led by Prokop 
the Great and Prokop the Less, who both fell in the battle, 
was totally defeated and almost annihilated at Lipan. The 
moderate party thus obtained the upper hand; and it formulated 
its demands in a document which was finally accepted by the 
Church of Rome in a slightly modified form, and which is known 
as " the compacts." The compacts, mainly founded on the 
articles of Prague, declare that: — 

1. The Holy Sacrament is to be given freely in both kinds to all 
Christians in Bohemia and Moravia, and to those elsewhere who 
adhere to the faith of these two countries. 

2. All mortal sins shall be punished and extirpated by those whose 
office it is so to do. 

3. The word of God is to be freely and truthfully preached by the 
priests of the Lord, and by worthy deacons. 

4. The priests in the time of the law of grace shall claim no owner- 
ship of worldly possessions. 

On the 5th of July 1436 the compacts were formally accepted 
and signed at Iglau, in Moravia, by King Sigismund, by the 
Hussite delegates, and by the representatives of the Roman 
Church. The last-named, however, refused to recognize as 
archbishop of Prague, John of Rokycan, who had been elected 
to that dignity by the estates of Bohemia. The Utraquist 
creed, frequently varying in its details, continued to be that 
of the established church of Bohemia till all non-Roman religious 
services were prohibited shortly after the battle of the White 
Mountain in 1620. The .Taborite party never recovered from 
its defeat at Lipan, and after the town of Tabor had been captured 
by George of Podebrad in 1452 Utraquist religious worship was 
established there. The Bohemian brethren, whose intellectual 
originator was Peter Cheldcky, but whose actual founders 
were Brother Gregory, a nephew of Archbishop Rokycan, 
and Michael, curate of Zamberk, to a certain extent continued 
the Taborite traditions, and in the 15th and 16th centuries 
included most of the strongest opponents of Rome in Bohemia. 
J. A. Komensky (Comenius), a member of the brotherhood, 
claimed for the members of his church that they were the genuine 
inheritors of the doctrines of Hus. After the beginning of the 
German Reformation many Utraquists adopted to a large 
extent the doctrines of Luther and Calvin; and in 1567 obtained 
the repeal of the compacts, which no longer seemed sufficiently 
far-reaching. From the end of the 16th century the inheritors 
of the Hussite tradition in Bohemia were included in the more 
general name of " Protestants " borne by the adherents of the 
Reformation. 



All histories of Bohemia devote a large amount of space to the 
Hussite movement. See Count Ltitzow, Bohemia; an Historical 
Sketch (London, 1896); Palacky, Geschichte von Bbhmen; Bach- 
mann, Geschichte Bbhmens; L. Krummel, Geschichte der bbhmischen 
Reformation (Gotha, 1866) and Vtraquisten und Taboriten (Gotha, 
1 871); Ernest Denis, Huss et la guerre des Hussites (Paris, 1878); 
H. Toman, Husitske Vdlecnictvi (Prague, 1898). (L.) 

HUSTING (O. Eng. husting, from Old Norwegian husthing), 
the " thing " or " ting," i.e. assembly, of the household of 
personal followers or retainers of a king, earl or chief, contrasted 
with the " folkmoot," the assembly of the whole people. "Thing" 
meant an inanimate object, the ordinary meaning at the present 
day, also a cause or suit, and an assembly; a similar develop- 
ment of meaning is found in the Latin res. The word still 
appears in the names of the legislative assemblies of Norway, 
the Storthing and of Iceland, the Althing. " Husting," or 
more usually in the plural " hustings," was the name of a court 
of the city of London. This court was formerly the county 
court for the city and was held before the lord mayor, the 
sheriffs and aldermen, for pleas of land, common pleas and 
appeals from the sheriffs. It had probate jurisdiction and wills 
were registered. All this jurisdiction has long been obsolete, 
but the court still sits occasionally for registering gifts made to 
the city. The charter of Canute (1032) contains a reference 
to " hustings " weights, which points to the early establishment 
of the court. It is doubtful whether courts of this name were 
held in other towns, but John Cowell (1554-1611) in his Inter- 
preter (1601) s.v., "Hustings," says that according to Fleta there 
were such courts at Winchester, York, Lincoln, Sheppey and 
elsewhere, but the passage from Fleta, as the New English 
Dictionary points out, does not necessarily imply this (n. lv. 
Habet etiam Rex curiam in civitatibus . . . et in locis . . . 
sicut in Hustingis London, Winton, cVc). The ordinary use 
of " hustings " at the present day for the platform from which 
a candidate sDeaks at a parliamentary or other election, or 
more widely for a political candidate's election campaign, is 
derived from the application of the word, first to the platform 
in the Guildhall on which the London court was held, and next 
to that from which the public nomination of candidates for a 
parliamentary election was formerly made, and from which 
the candidate addressed the electors. The Ballot Act of 1872 
did away with this public declaration of the nomination. 

HUSUM, a town in the Prussian province of Schleswig-Holstein, 
in a fertile district 23 m. inland from the North Sea, on the 
canalized Husumer Au, which forms its harbour and roadstead, 
99 m. N.W. from Hamburg on a branch line from Tonning. 
Pop. (1900) 8268. It has steam communication with the 
North Frisian Islands (Nordstrand, Fohr and Sylt), and is a 
port for the cattle trade with England. Besides a ducal palace 
and park, it possesses an Evangelical church and a gymnasium. 
Cattle markets are held weekly, and in them, as also in cereals, 
a lively export trade is done. There are also extensive oyster 
fisheries, the property of the state, the yield during the season 
being very considerable. Husum is the birthplace of Johann 
Georg Forchhammer (1794-^65), the mineralogist, Peter 
Wilhelm Forchhammer (1801-1894), the archaeologist, and 
Theodore Storm (1817-1888), the poet, to the last of whom a 
monument has been erected here. 

Husum is first mentioned in 1252, and its first church was 
built in 1431. Wisby rights were granted it in 1582, and in 
1603 it received municipal privileges from the duke of Holstein. 
It suffered greatly from inundations in 1634 and 171 7. 

See Christiansen, Die Geschichte Husums (Husum, 1903) ;. and 
Henningsen, Das Stiftungsbuch der Stadt Husum (Husum, 1904). ~* 

HUTCHESON, FRANCIS (1694-1746), English philosopher, 
was born on the 8th of August 1694. His birthplace was probably 
the townland of Drumalig, in the parish of Saintfield and county 
of Down, Ireland. 1 Though the family had sprung from Ayrshire, 
in Scotland, both his father and grandfather were ministers 
of dissenting congregations in the north of Ireland. Hutcheson 
was educated partly by his grandfather, partly at an academy, 
where according to his biographer, Dr Leechman, he was taught 
1 See Belfast Magazine for August 1813. 



IO 



HUTCHESON 



" the ordinary scholastic philosophy which was in vogue in 
those days." In 1710 he entered the university of Glasgow, 
where he spent six years, at first in the study of philosophy, 
classics and general literature, and afterwards in the study 
of theology. On quitting the university, he returned to the 
north of Ireland, and received a licence to preach. When, 
however, he was about to enter upon the pastorate of a small 
dissenting congregation he changed his plans on the advice 
of a friend and opened a private academy in Dublin. In Dublin 
his literary attainments gained him the friendship of many 
prominent inhabitants. Among these was Archbishop King 
(author of the De arigine mall), who resisted all attempts to 
prosecute Hutcheson in the archbishop's court for keeping a 
school without the episcopal licence. Hutcheson's relations 
with the clergy of the Established Church, especially with the 
archbishops of Armagh and Dublin, Hugh Boulter (1672-1742) 
and William King (1650-1729), seem to have been most cordial, 
and his biographer, in speaking of " the inclination of his friends 
to serve him, the schemes proposed to him for obtaining pro- 
motion," &c, probably refers to some offers of preferment, on 
condition of his accepting episcopal ordination. These offers, 
however, were unavailing. 

While residing in Dublin, Hutcheson published anonymously 
the four essays by which he is best known, namely, the Inquiry 
concerning Beauty, Order, Harmony and. Design, the Inquiry con- 
cerning Moral Good and Evil, in 1725, the Essay on the Nature 
and Conduct of the Passions and AJfections and Illustrations 
upon the Moral Sense, in 1728. The alterations and additions 
made in the second edition of these Essays were published in a 
separate form in 1726. To the period of his Dublin residence 
are also to be referred the Thoughts on Laughter (a criticism of 
Hobbes) and the Observations on the Fable of the Bees, being 
in all six letters contributed to Hibernicus' Letters, a periodical 
which appeared in Dublin (1725-1727, 2nd ed. 1734). Attheend 
of the same period occurred the controversy in the London 
Journal with Gilbert Burnet (probably the second son of Dr 
Gilbert Burnet, bishop of Salisbury); on the " True Foundation 
of Virtue or Moral Goodness." All these letters were collected 
in one volume (Glasgow, 1772). 

In 1729 Hutcheson succeeded his old master, Gershom 
Carmichael, in the chair of moral philosophy in the university 
of Glasgow. It is curious that up to this time all his essays 
and letters had been published anonymously, though their 
authorship appears to have been well known. In 1730 he 
entered on the duties of his office, delivering an inaugural lecture 
(afterwards published), De naturali hominum socialitate. 
It was a great relief to him after the drudgery of school work 
to secure leisure for his favourite studies; " non levi igitur 
laetitia commovebar cum almam matrem Academiam me, 
suum olim alumnum, in libertatem asseruisse audiveram." 
Yet the works on which Hutcheson's reputation rests had 
already been published. 

The remainder of his life he devoted to his professorial 
duties. His reputation as a teacher attracted many young 
men, belonging to dissenting families, from England and Ireland, 
and he enjoyed a well-deserved popularity among both his 
pupils and his colleagues. Though somewhat quick-tempered, 
he was remarkable for his warm feelings and generous impulses. 
He was accused in 1738 before the Glasgow presbytery for 
" following two false and dangerous doctrines: first, that the 
standard of moral goodness was the promotion of the happiness 
of others; and second, that we could have a knowledge of good 
and evil without and prior to a knowledge of God" (Rae, Life 
of Adam Smith, 1895). The accusation seems to have had no 
result. 

In addition to the works named, the following were published 
during Hutcheson's lifetime: a pamphlet entitled Considerations 
on Patronage (1735); Philosophiae moralis institutio com- 
pendiaria, ethices et jurisprudentiae naturalis elementa continens, 
lib. Hi. (Glasgow, 1742); Metaphysicae synapsis ontologiam 
et pneumatologiam complectens (Glasgow, 1742). The last 
work was published anonymously. After his death, his son, 



Francis Hutcheson (c. 1722-1773), author of a number of 
popular songs (e.g. " As Colin one evening," " Jolly Bacchus," 
" Where Weeping Yews "), published much the longest, though 
by no means the most interesting, of his works, A System of 
Moral Philosophy, in Three Books (2 vols. , London, 1755). To this 
is prefixed a life of the author, by Dr William Leechman (1706- 
1785), professor of divinity in the university of Glasgow. The 
only remaining work assigned to Hutcheson is a small treatise on 
Logic (Glasgow, 1 764) . This compendium, together with the Com- 
pendium of Metaphysics, was republished at Strassburg in 1722. 
Thus Hutcheson dealt with metaphysics, logic and ethics. 
His importance is, however, due almost entirely to his ethical 
writings, and among these primarily to the four essays and the 
letters published during his residence in Dublin. His standpoint 
has a negative and a positive aspect; he is in strong opposition 
to Thomas Hobbes and Bernard de Mandeville, and in funda- 
mental agreement with Shaftesbury (Anthony Ashley Cooper, 
3rd earl of Shaftesbury), whost name he very properly coupled 
with his own on the title-page of the first two essays. There 
are no two names, perhaps, in the histywy of English moral 
philosophy, which stand in a closer connexion. The analogy 
drawn between beauty and virtue, the functions assigned to 
the moral sense, the position that the benevolent feelings form 
an original and irreducible part of our nature, and the unhesitating 
adoption of the principle that the test of virtuous action is its 
tendency to promote the general welfare are obvious and funda- 
mental points of agreement between the two authors. 

I. Ethics. — According to Hutcheson, man has a variety of senses, 
internal as well as external, reflex as well as direct, the general 
definition of a sense being " any determination of our minds to receive 
ideas independently on our will, and to have perceptions of pleasure 
and pain " (Essay on the Nature and Conduct of the Passions, sect. 1). 
He does not attempt to give an exhaustive enumeration of these 
" senses," but, in various parts of his works, he specifies, besides the 
five external senses commonly recognized (which, he rightly hints, 
might be added to), — (1) consciousness, by which each man has a 
perception of himself and of all that is going on in his own mind 
(Metaph. Syn. pars i. cap. 2) ; (2) the sense of beauty (sometimes 
called specifically " an internal sense ") ; (3) a public sense, or sensus 
communis, " a determination to be pleased with the happiness of 
others and to be uneasy at their misery "; (4) the moral sense, or 
" moral sense of beauty in actions and affections, by which we 
perceive virtue or vice, in ourselves or others " ; (5) a sense of honour, 
or praise and blame, " which makes the approbation or gratitude of 
others the necessary occasion of pleasure, and their dislike, con- 
demnation or resentment of injuries done by us the occasion of that 
uneasy sensation called shame"; (6) a sense of the ridiculous. It 
is plain, as the author confesses, that there may be " other percep- 
tions, distinct from all these classes," and, in fact, there seems to be 
no limit to the number of " senses " in which a psychological division 
of this kind might result. 

Of these " senses " that which plays the most important part in 
Hutcheson's ethical system is the " moral sense." It is this which 
pronounces immediately on the character of actions and affections, 
approving those which are virtuous, and disapproving those which 
are vicious. " His principal design," he says in the preface to the 
two first treatises, " is to show that human nature was not left quite 
indifferent in the affair of virtue, to form to itself observations con- 
cerning the advantage or disadvantage of actions, and accordingly to 
regulate its conduct. The weakness of our reason, and the avocations 
arising from the infirmity and necessities of our nature, are so great 
that very few men could ever have formed those long deductions of 
reasons which show some actions tc be in the whole advantageous 
to the agent, and their contraries pernicious. The Author of nature 
has much better furnished us for a virtuous conduct than our 
moralists seem to imagine, by almost as quick and powerful instruc- 
tions as we have for the preservation of our bodies. He has made 
virtue a lovely form, to excite our pursuit of it, and has given us 
strong affections to be the springs of each virtuous action." Passing 
over the appeal to final causes involved in this and similar passages, 
as well as the assumption that the " moral sense " has had no growth 
or history, but was " implanted " in man exactly in the condition in 
which it is now to be found among the more civilized races, an 
assumption common to the systems of both Hutcheson and Butler, 
it may be remarked that this use of the term " sense " has a tendency 
to obscure the real nature of the process which goes on in an act of 
moral judgment. For, as is so clearly established by Hume, this act 
really consists of two parts: one an act of deliberation, more or less 
prolonged, resulting in an intellectual judgment; the other a reflex 
feeling, probably instantaneous, of satisfaction at actions which we 
denominate good, of dissatisfaction at those which we denominate bad. 
By the intellectual part of this process we refer the action or habit 
to a certain class ; but no sooner is the intellectual process completed 



HUTCHESON 



ii 



than there is excited in us a feeling similar to that which myriads of 
actions and habits of the same class, or deemed to be of the same 
class, have e.xcited in us on former occasions. Now, supposing the 
latter part of this process to be instantaneous, uniform and exempt 
from error, the former certainly is not. All mankind may, apart from 
their selfish interests, approve that which is virtuous or makes for 
the general good, but surely they entertain the most widely divergent 
opinions, and, in fact, freq jently arrive at directly opposite con- 
clusions as to particular actions and habits. This obvious distinction 
is undoubtedly recognized by Hutcheson in his analysis of the mental 
process preceding moral action, nor does he invariably ignore it, 
even when treating of the moral approbation or disapprobation which 
is subsequent on action. None the less, it remains true that 
Hutcheson, both by his phraseology, and by the language in which he 
describes the process of moral approbation, has done much to favour 
that loose, popular view of morality which, ignoring the necessity of 
deliberation and reflection, encourages hasty resolves and unpre- 
meditated judgments. The term " moral sense " (which, it may be 
noticed, had already been employed by Shaftesbury, not only, as Dr 
Whewell appears to intimate, in the margin, but also in the text of his 
Inquiry), if invariably coupled with the term " moral judgment," 
would be open to little objection; but, taken alone, as designating 
the complex process of moral approbation, it is liable to lead not 
only to serious misapprehension but to grave practical errors. For, 
if each man's decisions are solely the result of an immediate intuition 
of the moral sense, why be at any pains to test, correct or review 
them? Or why educate a faculty whose decisions are infallible? 
And how do we account for differences in the moral decisions of 
different societies, and the observable changes in a man's own 
views? The expression has, in fact, the fault of most metaphorical 
terms: it leads to an exaggeration of the truth which it is intended 
to suggest. 

But though Hutcheson usually describes the moral faculty as 
acting instinctively and immediately, he does not, like Butler, con- 
found the moral faculty with the moral standard. The test or 
criterion of right action is with Hutcheson, as with Shaftesbury, its 
tendency to promote the general welfare of mankind. He thus 
anticipates the utilitarianism of Bentham — and not only in principle, 
but even in the use of the phrase " the greatest happiness for the 
greatest number " (Inquiry concerning Moral Good and Evil, sect. 3). 
It is curious that Hutcheson did not realize the inconsistency of 
this external criterion with his fundamental ethical principle. In- 
tuition has no possible connexion with an empirical calculation of 
results, and Hutcheson in adopting such a criterion practically 
denies his fundamental assumption. 

As connected with Hutcheson's virtual adoption of the utilitarian 
standard may be noticed a kind of moral algebra, proposed for the 
purpose of " computing the morality of actions." This calculus 
occurs in the Inquiry concerning Moral Good and Evil, sect. 3. 

The most distinctive of Hutcheson's ethical doctrines still remaining 
to be noticed is what has been called the " benevolent theory " of 
morals. Hobbes had maintained that all our actions, how- 
ever disguised under apparent sympathy, have their roots in 
self-love. Hutcheson not only maintains that benevolence 
is the sole and direct source of many of our actions, but, by a not un- 
natural recoil, that it is the only source of those actions of which, on 
reflection, we approve. Consistently with this position, actions which 
flow from self-love only are pronounced to be morally indifferent. 
But surely, by the common consent of civilized men, prudence, 
temperance, cleanliness, industry, self-respect and, in general, the 
'" personal virtues," are regarded, and rightly regarded, as fitting 
objects of moral approbation. This consideration could hardly escape 
any author, however wedded to his own system, and Hutcheson 
attempts to extricate himself from the difficulty by laying down the 
position that a man may justly regard himself as a part of the rational 
system, and may thus " be, in part, an object of his own benevo- 
lence " (Ibid.), — a curious abuse of terms, which really concedes the 
question at issue. Moreover, he acknowledges that, though self-love 
does not merit approbation, neither, except in its extreme forms, does 
it merit condemnation, indeed the satisfaction of the dictates of self- 
love is one.of the very conditions of the preservation of society. To 
press home the inconsistencies involved in these various statements 
would be a superfluous task. 

The vexed question of liberty and necessity appears to be carefully 
avoided in Hutcheson's professedly ethical works. But, in the 
Synopsis metaphysical, he touches on it in three places, briefly 
stating both sides of the question, but evidently inclining to that 
which he designates as the opinion of the Stoics in opposition to 
what he designates as the opinion of the Peripatetics. This is 
substantially the same as the doctrine propounded by Hobbes and 
Locke (to the latter of whom Hutcheson refers in a note), namely, 
that our will is determined by motives in conjunction with our 
general character and habit 'of mind, and that the only true liberty 
is the liberty of acting as we will, not the liberty of willing as we will. 
Though, however, his leaning is clear, he carefully avoids dogmatiz- 
ing, and deprecates the angry controversies to which the speculations 
on this subject had given rise. 

It is easy to trace ihe influence of Hutcheson's ethical theories on 
the systems of Hume and Adam Smith. The prominence given by 
these writers to the analysis of moral action and moral approbation, 



Benevo- 
lence. 



with the attempt to discriminate the respective provinces of the 
reason and the emotions in these processes, is undoubtedly due to the 
influence of Hutcheson. To a study of the writings of Shaftesbury 
and Hutcheson we might, probably, in large measure, attribute the 
unequivocal adoption of the utilitarian standard by Hume, and, if 
this be the case, the name of Hutcheson connects itself, through 
Hume, with the names of Priestley, Paley and Bentham. Butler's 
Sermons appeared in 1726, the year after the publication of 
Hutcheson's two first essays, and the parallelism between the 
" conscience " of the one writer and the " moral sense " of the othet 
is, at least, worthy of remark. 

II. Mental Philosophy. — In the sphere of mental philosophy and 
logic Hutcheson's contributions are by no means so important or 
original as in that of moral philosophy. They are interesting mainly 
as a link between Locke and the Scottish school. In the former 
subject the influence of Locke is apparent throughout. All the main 
outlines of Locke's philosophy seem, at first sight, to be accepted as a 
matter of course. Thus, in stating his theory of the moral sense, 
Hutcheson is peculiarly careful to repudiate the doctrine of innate 
ideas (see, for instance, Inquiry concerning Moral Good and Evil, sect. 
1 ad fin., and sect. 4; and compare Synopsis Metaphysicae, pars i. 
cap. 2). At the same time he shows more discrimination than does 
Locke in distinguishing between the two uses of this expression, and 
between the legitimate and illegitimate form of the doctrine (Syn. 
Metaph. pars i. cap. 2). All our ideas are, as by Locke, referred to 
external or internal sense, or, in other words, to sensation and re- 
flection (see, for instance, Syn. Metaph. pars i. cap. I ; Logicae 
Compend. pars i. cap. 1; System of Moral Philosophy, bk. i. ch. 1). 
It is, however, a most important modification of Locke's doctrine, 
and one which connects Hutcheson's mental philosophy with that of 
Reid, when he states that the ideas of extension, figure, motion and 
rest "are more properly ideas accompanying the sensations of sight 
and touch than the sensations of either of these senses "; that the 
idea of self accompanies every thought, and that the ideas of 
number, duration and existence accompany every other idea what- 
soever (see Essay on the Nature and Conduct of the Passions, sect. i. 
art. 1; Syn. Metaph. pars i. cap. I, pars ii. cap. 1; Hamilton on 
Reid, p. 124, note). Other important points in which Hutcheson 
follows the lead of Locke are his depreciation of the importance of 
the so-called laws of thought, his distinction between the primary and 
secondary qualities of bodies, the position that we cannot know the 
inmost essences of things (" intimae rerum naturae sive essentiae "), 
though they excite various ideas in us, and the assumption that ex- 
ternal things are known only through the medium of ideas (Syn. 
Metaph. pars i. cap. 1), though, at the same time, we are assured 
of the existence of an external world corresponding to these ideas. 
Hutcheson attempts to account for our assurance of the reality of 
an external world by referring it to a natural instinct (Syn. Metaph. 
pars i. cap_. 1). Of the correspondence or similitude between our ideas 
of the primary qualities of things and the things themselves God 
alone can be assigned as the cause. This similitude has been effected 
by Him through a law of nature. " Haec prima qualitatum prima- 
riarum perceptio, sive mentis actio quaedam sive passio dicatur, non 
alia similitudinis aut convenientiae inter ejusmodi ideas et res ipsas 
causa assignari posse videtur, quam ipse Deus, qui certa naturae lege 
hoc efficit, ut notiones, quae rebus praesentibus excitantur, sint ipsis 
similes, aut saltern earum habitudines, si non veras quantitates, 
depingant " (pars ii. cap. 1). Locke does speak of God " annexing " 
certain ideas to certain motions of bodies; but nowhere does he 
propound a theory so definite as that here propounded by Hutcheson, 
which reminds us at least as much of the speculations of Malebranche 
as of those of Locke. 

Amongst the more important points in which Hutcheson diverges 
from Locke is his account of the idea of personal identity, which he 
appears to have regarded as made known to us directly by conscious- 
ness. The distinction between body and mind, corpus or materia and 
res cogitans, is more emphatically accentuated by Hutcheson than 
by Locke. Generally, he speaks as if we had a direct consciousness 
of mind as distinct from body (see, for instance, Syn. Metaph. -pars ii. 
cap. 3), though, in the posthumous work on Moral Philosophy, he 
expressly states that we know mind as we know body " by qualities 
immediately perceived though the substance of both be unknown " 
(bk. i. ch. 1). The distinction between perception proper and sensa- 
tion proper, which occurs by implication though it is not explicitly 
worked out (see Hamilton's Lectures on Metaphysics,. Lect. 24; 
Hamilton's edition of Dugald Stewart's Works, v. 420),- the 
imperfection of the ordinary division of the external senses into five 
classes, the limitation of consciousness to a special mental faculty 
(severely criticized in Sir W. Hamilton's Lectures on Metaphysics, 
Lect. xii.) and the disposition to refer on disputed questions of philo- 
sophy not so much to formal arguments as to the testimony of con- 
sciousness and our natural instincts are also amongst the points in 
which Hutcheson supplemented or departed from the philosophy of 
Locke. The last point can hardly fail to suggest the " common- 
sense philosophy " of Reid. 

Thus, in estimating Hutcheson's position, we find that in particular 
questions he stands nearer to Locke, but in the general spirit of his 
philosophy he seems to approach more closely to his Scottish suc- 
cessors. 

The short Compendium of Logic, which is more original than such 



12 



HUTCHINSON, ANNE— HUTCHINSON, JOHN 



works usually are, is remarkable chiefly for the large proportion of 
psychological matter which it contains. In these parts of the book 
Hutcheson mainly follows Locke. The technicalities of the subject 
are passed lightly over, and the book is readable. It may be specially 
noticed that he distinguishes between the mental result and its verbal 
expression [idea — term; judgment — proposition], that he constantly 
employs the word " idea," and that he defines logical truth as " con- 
venientia signorum cum rebus significatis " (or " propositionis con- 
venientia cum rebus ipsis," Syn. Metaph. pars i. cap 3), thus im- 
plicitly repudiating a merely formal view of logic. 

III. Aesthetics. — Hutcheson may further be regarded as one of 
the earliest modern writers on aesthetics. His speculations on this 
subject are contained in the Inquiry concerning Beauty, Order, 
Harmony and Design, the first of the two treatises published in 1725.. 
He maintains that we are endowed with a special sense by which we 
perceive beauty, harmony and proportion. This is a reflex sense, 
because it presupposes the action of the external senses of sight and 
hearing. It may be called an internal sense, both in order to dis- 
tinguish its perceptions from the mere perceptions of sight and 
hearing, and because " in some other affairs, where our external senses 
are not much concerned, we discern a sort of beauty, very like in 
many respects to that observed in sensible objects, and accompanied 
with like pleasure " {Inquiry, &c, sect. 1). The latter reason leads 
him to call attention to the beauty perceived in universal truths, in the 
operations of general causes and in moral principles and actions. 
Thus, the analogy between beauty and virtue, which was so favourite 
a topic with Shaftesbury, is prominent in the writings of Hutcheson 
also. Scattered up and down the treatise there are many important 
and interesting observations which our limits prevent us from 
noticing. But to the student of mental philosophy it may be 
specially interesting to remark that Hutcheson both applies the 
principle of association to explain our ideas of beauty and also sets 
limits to its application, insisting on there being " a natural power 
of perception or sense of beauty in objects, antecedent to all custom, 
education or example" (see Inquiry, &c, sects. 6, 7; Hamilton's 
Lectures on Metaphysics, Lect. 44 ad fin.). 

Hutcheson's writings naturally gave rise to much controversy. 
To say nothing of minor opponents, such as " Philaretus " (Gilbert 
Burnet, already alluded to), Dr John Balguy (1686-1748), pre- 
bendary of Salisbury, the author of two tracts on " The Foundation 
of Moral Goodness, ' and Dr John Taylor (1694-1761) of Norwich, a 
minister of considerable reputation in his time (author olAn Examina- 
tion of the Scheme of Morality advanced by Dr Hutcheson) , the essays 
appear to have suggested, by antagonism, at least two works which 
hold a permanent place in the literature of English ethics — Butler's 
Dissertation on the Nature of Virtue, and Richard Price's Treatise of 
Moral Good and Evil (1757). In this latter work the author main- 
tains, in opposition to Hutcheson, that actions are in themselves right 
or wrong, that right and wrong are simple ideas incapable of analysis, 
and that these ideas are perceived immediately by the understand- 
ing. We thus see that, not only directly but also through the replies 
which it called forth, the system of Hutcheson, or at least the system 
of Hutcheson combined with that of Shaftesbury, contributed, in 
large measure, to the formation and development of some of the most 
important of the modern schools of ethics (see especially art. Ethics). 
Authorities. — Notices of Hutcheson occur in most histories, both 
of general philosophy and of moral philosophy, as, for instance, in 
pt. vii. of Adam Smith's Theory of Moral Sentiments; Mackintosh's 
Progress of Ethical Philosophy; Cousin, Cours d'histoire de la 
philosophic morale du XV III" Steele; Whewell's Lectures on the 
History of Moral Philosophy in England; A. Bain's Mental and Moral 
Science; Noah Porter's Appendix to the English translation of 
Ueberweg's History of Philosophy; Sir Leslie Stephen's History of 
English Thought in the Eighteenth Century, &c. See also Martineau, 
Types of Ethical Theory (London, 1902) ; W. R. Scott, Francis 
Hutcheson (Cambridge, 1900) ; Albee, History of English Utilitarian- 
ism (London, 1902) ; T. Fowler, Shaftesbury and Hutcheson (London, 
1882); J. McCosh, Scottish Philosophy (New York, 1874). Of Dr 
Leechman's Biography of Hutcheson we have already spoken. 
J. Veitch gives an interesting account of his professorial work in 
Glasgow, Mind, ii. 209-212. (T. F. ; X.) 

HUTCHINSON, ANNE (c. 1 600-1 643), American religious 
enthusiast, leader of the " Antinomians " in New England, 
was born in Lincolnshire, England, about 1600. She was the 
daughter of a clergyman named Francis Marbury, and, according 
to tradition, was a cousin of John Dryden. She married William 
Hutchinson, and in 1634 emigrated to Boston, Massachusetts, 
as a follower and admirer of the Rev. John Cotton. Her orthodoxy 
was suspected and for a time she was not admitted to the church, 
but soon she organized meetings among the Boston women, 
among whom her exceptional ability and her services as a nurse 
had given her great influence; and at these meetings she dis- 
cussed and commented upon recent sermons and gave expression 
to her own theological views. The meetings became increasingly 
popular, and were soon attended not only by the women but 



even by some of the ministers and magistrates, including Governoi 
Henry Vane. At these meetings she asserted that she, Cotton 
and her brother-in-law, the Rev. John Wheelwright — whom 
she was trying to make second " teacher " in the Boston church — 
were under a " covenant of grace," that they had a special 
inspiration, a " peculiar indwelling of the Holy Ghost," whereas 
the Rev. John Wilson, the pastor of the Boston church, and 
the other ministers of the colony were under a " covenant of 
works." Anne Hutchinson was, in fact, voicing a protest against 
the legalism of the Massachusetts Puritans, and was also striking 
at the authority of the clergy in an intensely theocratic community. 
In such a community a theological controversy inevitably 
was carried into secular politics, and the entire colony was 
divided into factions. Mrs Hutchinson was supported by 
Governor Vane, Cotton, Wheelwright and the great majority of 
the Boston church; opposed to her were Deputy-Governor John 
Winthrop, Wilson and all of the country magistrates and 
churches. At a general fast, held late in January 1637, Wheel- 
wright preached a sermon which was taken as a criticism of 
Wilson and his friends. The strength of the parties was tested 
at the General Court of Election of May 1637, when Winthrop 
defeated Vane for the governorship. Cotton recanted, Vane re- 
turned to England in disgust, Wheelwright was tried and banished 
and the rank and file either followed Cotton in making sub- 
mission or suffered various minor punishments. Mrs Hutchinson 
was tried (November 1637) by the General Court chiefly for 
" traducing the ministers," and was sentenced to banishment; 
later, in March 1638, she was tried before the Boston church 
and was formally excommunicated. With William Coddington 
(d. 1678), John Clarke and others, she established a settlement 
on the island of Aquidneck (now Rhode Island) in 1638. Four 
years later, after the death of her husband, she settled on Long 
Island Sound near what is now New Rochelle, Westchester 
county, New York, and was killed in an Indian rising in August 
1643, an event regarded. in Massachusetts as a manifestation 
of Divine Providence. Anne Hutchinson and her followers 
were called " Antinomians," probably more as a term of reproach 
than with any special reference to her doctrinal theories; and 
the controversy in which she was involved is known as the 
" Antinomian Controversy." 

See C. F. Adams, Antinomianism in the Colony of Massachusetts 
Bay, vol. xiv. of the Prince Society Publications (Boston, 1894); 
and Three Episodes of Massachusetts History (Boston and New York, 
1896). 

HUTCHINSON, JOHN (1615-1664), Puritan soldier, son of 
Sir Thomas Hutchinson of Owthorpe, Nottinghamshire, and 
of Margaret, daughter of Sir John Byron of Newstead, was 
baptized on the 18th of September 1615. He was educated at 
Nottingham and Lincoln schools and at Peterhouse, Cambridge, 
and in 1637 he entered Lincoln's Inn. On the outbreak of the 
great Rebellion he took the side of the Parliament, and was 
made in 1643 governor of Nottingham Castle, which he defended 
against external attacks and internal divisions, till the triumph 
of the parliamentary cause. He was chosen member for 
Nottinghamshire in March 1646, took the side of the Independents, 
opposed the offers of the king at Newport, and signed the death- 
warrant. Though a member at first of the council of state, he 
disapproved of the subsequent political conduct of Cromwell 
and took no further part in politics during the lifetime of the 
protector. He resumed his seat in the recalled Long Parliament 
in May 1659, and followed Monk in opposing Lambert, believing 
that the former intended to maintain the commonwealth. 
He was returned to the Convention Parliament for Nottingham 
but expelled on the 9th of June 1660, and while not excepted 
from the Act of Indemnity was declared incapable of holding 
public office. In October 1663, however, he was arrested upon 
suspicion of being concerned in the Yorkshire plot, and after 
a rigorous confinement in the Tower of London, of which he 
published an account (reprinted in the Harleian Miscellany, 
vol. iii.), and in Sandown Castle, Kent, he died on the nth of 
September 1664. His career draws its chief interest from the 
Life by his wife, Lucy, daughter of Sir Allen Apsley. written 



HUTCHINSON, JOHN— HUTCHINSON 



1 3 



after the death of her husband but not published till 1806 (since 
often reprinted), a work not only valuable for the picture which 
it gives of the man and of the time in which he lived, but for 
the simple beauty of its style, and the naivete with which the 
writer records her sentiments and opinions, and details the 
incidents of her private life. 

See the edition of Lucy Hutchinson's Memoirs of the Life of Colonel 
Hutchinson by C. H. Firth (1885); Brit. Mus. Add. MSS. 25,901 (a 
fragment of the Life), also Add. MSS. 19, 333, 36,247 f. 51 ; Notes 
and Queries, 7, ser. iii. 25, viii. 422 ; Monk's Contemporaries, by 
Guizot. 

HUTCHINSON, JOHN (1674-1737), English theological writer, 
was born at Spennithorne, Yorkshire, in 1674. He served as 
steward in several families of position, latterly in that of the 
duke of Somerset, who ultimately obtained for him the post 
of riding purveyor to the master of the horse, a sinecure worth 
about £200 a year. In 1700 he became acquainted with Dr 
John Woodward (1665-1728) physician to the duke and author 
of a work entitled The Natural History of the Earth, to whom he 
entrusted a large number of fossils of his own collecting, along 
with a mass of manuscript notes, for arrangement and publication. 
A misunderstanding as to the manner in which these should 
be dealt with was the immediate occasion of the publication 
by Hutchinson in 1724 of Moses's Principia, part i., in which 
Woodward's Natural History was bitterly ridiculed, his conduct 
with regard to the mineralogical specimens not obscurely 
characterized, and a refutation of the Newtonian doctrine of 
gravitation seriously attempted. It was followed by part ii. 
in 1727, and by various other works, including Moses's Sine 
Principio, 1730; The Confusion of Tongues and Trinity of the 
Gentiles, 1731; Power Essential and Mechanical, or what power 
belongs to God and what to his creatures, in which the design of 
Sir I. Newton and Dr Samuel Clarke is laid open, 1732; Glory or 
Gravity, 1733; The Religion of Satan, or Antichrist Delineated, 
1736. He taught that the Bible contained the elements not only 
of true religion but also of all rational philosophy. He held 
that the Hebrew must be read without points, and his interpreta- 
tion rested largely on fanciful symbolism. Bishop George Home 
of Norwich was during some of his earlier years an avowed 
Hutchinsonian; and William Jones of Nayland continued to 
be so to the end of his life. 

A complete edition of his publications, edited by Robert Spearman 
and Julius Bate, appeared in 1748 (12 vols.); an Abstract of these 
followed in 1753; and a Supplement, with Life by Spearman pre- 
fixed, in 1765. 

HUTCHINSON, SIR JONATHAN (1828- ), English surgeon 
and pathologist, was born on the 23rd of July 1828 at Selby, 
Yorkshire, his parents belonging to the Society of Friends. 
He entered St Bartholomew's Hospital, became a member of the 
Royal College of Surgeons in 1850 (F.R.C.S. 1862), and rapidly 
gained reputation as a skilful operator and a scientific inquirer. 
He was president of the Hunterian Society in 1869 and 1870, 
professor of surgery and pathology at the College of Surgeons 
from 1877 to 1882, president of the Pathological Society, 1879- 
1880, of the Ophthalmological Society, 1883, of the Neurological 
Society, 1887, of the Medical Society, 1890, and of the Royal 
Medical and Chirurgical in 1894-1896. In 1889 he was president 
of the Royal College of Surgeons. He was a member of two 
Royal Commissions, that of 1881 to inquire into the provision 
for smallpox and fever cases in the London hospitals, and that 
of 1 889- 1 896 on vaccination and leprosy. He also acted as 
honorary secretary to the Sydenham Society. His activity 
in the cause of scientific surgery and in advancing the study 
of the natural sciences was unwearying. His lectures on neuro- 
pathogenesis, gout, leprosy, diseases of the tongue, &c, were full 
of original observation; but his principal work was connected 
with the study of syphilis, on which he became the first living 
authority. He was the founder of the London Polyclinic or 
Postgraduate School of Medicine; and both in his native town 
of Selby and at Haslemere, Surrey, he started (about 1890) 
educational museums for popular instruction in natural history. 
He published several volumes on his own subjects, was editor of 
the quarterly Archives of Surgery, and was given the Hon. LL.D. 



degree by both Glasgow and Cambridge. After his retirement 
from active consultative work he continued to take great interest 
in the question of leprosy, asserting the existence of a definite 
connexion between this disease and the eating of salted fish. 
He received a knighthood in 1908. 

HUTCHINSON, THOMAS (1711-1780), the last royal governor 
of the province of Massachusetts, son of a wealthy merchant 
of Boston, Mass., was born there on the 9th of September 1711. 
He graduated at Harvard in 1727, then became an apprentice 
in his father's counting-room, and for several years devoted 
himself to business. In 1737 he began his public career as a 
member of the Boston Board of Selectmen, and a few weeks 
later he was elected to the General Court of Massachusetts Bay, 
of which he was a member until 1740 and again from 1742 to 
1749, serving as speaker in 1747, 1748 and 1749. He con- 
sistently contended for a sound financial system, and vigorously 
opposed the operations of the " Land Bank " and the issue of 
pernicious bills of credit. In 1748 he carried through the 
General Court a bill providing for the cancellation and redemption 
of the outstanding paper currency. Hutchinson went to England 
in 1740 as the representative of Massachusetts in a boundary 
dispute with New Hampshire. He was a member of the Massa- 
chusetts Council from 1749 to 1756, was appointed judge of 
probate in 1752 and was chief justice of the superior court of 
the province from 1761 to 1769, was lieutenant-governor from 
1758 to 1 77 1, acting as governor in the latter two years, and 
from 1 771 to 1774 was governor. In 1754 he was a delegate 
from Massachusetts to the Albany Convention, and, with Franklin, 
was a member of the committee appointed to draw up a plan of 
union. Though he recognized the legality of the Stamp Act 
of 1765, he considered the measure inexpedient and impolitic 
and urged its repeal, but his attitude was misunderstood; he 
was considered by many to have instigated the passage of the 
Act, and in August 1765 a mob sacked his Boston residence 
and destroyed many valuable manuscripts and documents. 
He was acting governor at the time of the " Boston Massacre " 
in 1770, and was virtually forced by the citizens of Boston, 
under the leadership of Samuel Adams, to order the removal 
of the British troops from the town. Throughout the pre- 
Revolutionary disturbances in Massachusetts he was the re- 
presentative of the British ministry, and though he disapproved 
of some of the ministerial measures he felt impelled to enforce 
them and necessarily incurred the hostility of the Whig or 
Patriot element. In 1774, upon the appointment of General 
Thomas Gage as military governor he went to England, and 
acted as an adviser to George III. and the British ministry 
on American affairs, uniformly counselling moderation. He 
died at Brompton, now part of London, on the 3rd of June 
1780. 

He wrote A Brief Statement of the Claim of the Colonies (1764) ; a 
Collection of Original Papers relative to the History of Massachusetts 
Bay (1769), reprinted as The Hutchinson Papers by the Prince 
Society in 1865; and a judicious, accurate and very valuable History 
of the Province of Massachusetts Bay (vol. i., 1764, vol. ii., 1767, and 
vol. iii., 1828). His Diary and Letters, with an Account of his Ad- 
ministration, was published at Boston in 1 884-1 886. 

See James K. Hosmer's Life of Thomas Hutchinson (Boston, 1896), 
and a biographical chapter in John Fiske's Essays Historical and 
Literary (New York, 1902). For an estimate of Hutchinson as an 
historian, see M. C. Tyler's Literary History of the American Revolu- 
tion (New York, 1897). 

HUTCHINSON, a city and the county-seat of Reno county, 
Kansas, U.S.A., in the broad bottom-land on the N. side. of 
the Arkansas river. Pop. (1900) 9379, of whom 414 were 
foreign-born and 442 negroes; (1910 census) 16,364. It 
is served by the Atchison, Topeka & Santa Fe, the Missouri 
Pacific and the Chicago, Rock Island & Pacific railways. The 
principal public buildings are the Federal building and the county 
court house. The city has a public library, and an industrial 
reformatory is maintained here by the state. Hutchinson is 
situated in a stock-raising, fruit-growing and farming region 
(the principal products of which are wheat, Indian corn and 
fodder), with which it has a considerable wholesale trade. An 
■ enormous deposit of rock salt underlies the city and its vicinity, 



H 



HUTTEN, P. VON— HUTTEN, U. VON 



and Hutchinson's principal industry is the manufacture (by 
the open-pan and grainer processes) and the shipping of salt; 
the city has one of the largest salt plants in the world. Among 
the other manufactures are flour, creamery products, soda- 
ash, straw-board, planing-mill products and packed meats. 
Natural gas is largely used as a factory fuel. The city's factory 
product was valued at $2,031,048 in 1905, an increase of 31-8% 
since 1900. Hutchinson was chartered as a city in 1871. 

HUTTEN, PHILIPP VON (c. 1511-1546), German knight, 
was a relative of Ulrich von Hutten and passed some of his 
early years at the court of the emperor Charles V. Later he 
joined the band of adventurers which under Georg Hohermuth, 
or George of Spires, sailed to Venezuela, or Venosala as Hutten 
calls it, with the object of conquering and exploiting this land in 
the interests of the Augsburg family of Welser. The party 
landed at Coro in February 1535 and Hutten accompanied 
Hohermuth on his long and toilsome expedition into the interior 
in search of treasure. After the death of Hohermuth in December 
1540 he became captain-general of Venezuela. Soon after this 
event he vanished into the interior, returning after five years 
of wandering to find that a Spaniard, Juan de Caravazil, or 
Caravajil, had been appointed governor in his absence. With 
his travelling companion, Bartholomew Welser the younger, 
he was seized by CaravaziL in April 1546 and the two were 
afterwards put to death. 

Hutten left some letters, and also a narrative of the earlier part of 
his adventures, this Zeitung aus India Junkher Philipps von Hutten 
being published in 1785. 

HUTTEN, ULRICH VON (1488-1523), was born on the 21st of 

April 1488, at the castle of Steckelberg, near Fulda, in Hesse. 

Like Erasmus or Pirckheimer, he was one of those men who 

form the bridge between Humanists and Reformers. He lived 

with both, sympathized with both, though he died before the 

Reformation had time fully to develop. His life may be divided 

into four parts: — his youth and cloister-life (1488-1504); his 

wanderings in pursuit of knowledge (1 504-1 51 5); his strife 

with Ulrich of Wurttemberg (1515-1519); and his connexion 

with the Reformation (1 519-1523). Each of these periods 

had its own special antagonism, which coloured Hutten's career: 

in the first, his horror of dull monastic routine; in the second, 

the ill-treatment he met with at Greifswald; in the third, the 

crime of Duke Ulrich; in the fourth, his disgust with Rome 

and with Erasmus. He was the eldest son of a poor and not 

undistinguished knightly family. As he was mean of stature 

and sickly his father destined him for the cloister, and he was 

sent to the Benedictine house at Fulda; the thirst for learning 

there seized on him, and in 1505 he fled from the monastic life, 

and won his freedom with the sacrifice of his worldly prospects, 

and at the cost of incurring his father's undying anger. From 

the Fulda cloister he went first to Cologne, next to Erfurt, and then 

to Frankfort-on-Oder on the opening in 1 506 of the new university 

of that town. For a time he was in Leipzig, and in 1508 we find 

him a shipwrecked beggar on the Pomeranian coast. In 1509 

the university of Greifswald welcomed him, but here too those 

who at first received him kindly became his foes; the sensitive 

ill-regulated youth, who took the liberties of genius, wearied 

his burgher patrons; they could not brook the poet's airs and 

vanity, and ill-timed assertions of his higher rank. Wherefore 

he left Greifswald, and as he went was robbed of clothes and 

books, his only baggage, by the servants of his late friends; 

in the dead of winter, half starved, frozen, penniless, he reached 

Rostock. Here again the Humanists received him gladly, 

and under their protection he wrote against his Greifswald 

patrons, thus beginning the long list of his satires and fierce 

attacks on personal or public foes. Rostock could not hold 

him long; he wandered on to Wittenberg and Leipzig, and 

thence to Vienna, where he hoped to win the emperor Maximilian's 

favour by an elaborate national poem on the war with Venice. 

But neither Maximilian nor the university of Vienna would 

lift a hand for him, and he passed into Italy, where, at Pavia, 

he sojourned throughout 151 1 and part of 151 2. In the latter 

year his studies were interrupted by war; in the siege of Pavia 



by papal troops and Swiss, he was plundered by both sides, 
and escaped, sick and penniless, to Bologna; on his recovery 
he even took service as a private soldier in the emperor's army. 
This dark period lasted no long time; in 15 14 he was again 
in Germany, where, thanks to his poetic gifts and the friendship 
of Eitelwolf von Stein (d. 151 5), he won the favour of the elector 
of Mainz, Archbishop Albert of Brandenburg. Here high 
dreams of a learned career rose on him; Mainz should be made 
the metropolis of a grand Humanist movement, the centre of 
good style and literary form. But the murder in 1515 of his 
relative Hans von Hutten by Ulrich, duke of Wurttemberg, 
changed the whole course of his life; satire, chief refuge of the 
weak, became Hutten's weapon; with one hand he took his 
part in the famous Epistolae obscurorum virorum, and with 
the other launched scathing letters, eloquent Ciceronian orations, 
or biting satires against the duke. Though the emperor was 
too lazy and indifferent to smite a great prince, he took Hutten 
under his protection and bestowed on him the honour of a 
laureate crown -in 151 7. Hutten, who had meanwhile revisited 
Italy, again attached himself to the electoral court at Mainz; 
and he was there when in 1518 his friend Pirckheimer wrote, 
urging him to abandon the court and dedicate himself to letters. 
We have the poet's long reply, in an epistle on his " way of life," 
an amusing mixture of earnestness and vanity, self-satisfaction 
and satire; he tells his friend that his career is just begun, 
that he has had twelve years of wandering, and will now enjoy 
himself a while in patriotic literary work; that he has by no 
means deserted the humaner studies, but carries with him 
a little library of standard books. Pirckheimer in his burgher 
life may have ease and even luxury; he, a knight of the empire, 
how can he condescend to obscurity? He must abide where 
he can shine. 

In 1 519 he issued in one volume his attacks on Duke Ulrich, 
and then, drawing sword, took part in the private war which 
overthrew that prince; in this affair he became intimate with 
Franz von Sickingen, the champion of the knightly order 
(Ritterstand). Hutten now warmly and openly espoused the 
Lutheran cause, but he was at the same time mixed up in the 
attempt of the " Ritterstand " to assert itself as the militia 
of the empire against the independence of the German princes. 
Soon after this time he discovered at Fulda a copy of the mani- 
festo of the emperor Henry IV. against Hildebrand, and published 
it with comments as an attack on the papal claims over Germany. 
He hoped thereby to interest the new emperor Charles V., and 
the higher orders in the empire, in behalf of German liberties; 
but the appeal failed. What Luther had achieved by speaking 
to cities and common folk in homely phrase, because he touched 
heart and conscience, that the far finer weapons of Hutten failed 
to effect, because he tried to touch the more cultivated sympathies 
and dormant patriotism of princes and bishops, nobles and 
knights. And so he at once gained an undying name in the 
republic of letters and ruined his own career. He showed that 
the artificial verse-making of the Humanists could be connected 
with the new outburst of genuine German poetry. The Minne- 
singer was gone; the new national singer, a Luther or a Hans 
Sachs, was heralded by the stirring lines of Hutten's pen. These 
have in them a splendid natural swing and ring, strong and 
patriotic, though unfortunately addressed to knight and lands- 
knecht rather than to the German people. 

The poet's high dream of a knightly national regeneration 
had a rude awakening. The attack on the papacy, and Luther's 
vast and sudden popularity, frightened Elector Albert, who_ 
dismissed Hutten from his court. Hoping for imperial favour, 
he betook himself to Charles V.; but that young prince would 
have none of him. So he returned to his friends, and they 
rejoiced greatly to see him still alive; for Pope Leo X. had 
ordered him to be arrested and sent to Rome, and assassins 
dogged his steps. He now attached himself more closely to 
Franz von Sickingen and the knightly movement. This also 
came to a disastrous end in the capture of the Ebernberg, and 
Sickingen's death; the higher nobles had triumphed; the- 
archbishops avenged themselves on Lutheranism as interpreted 



HUTTER— HUTTON, C. 



15 



by the knightly order. With Sickingen Hutten also finally fell. 
He fled to Basel, where Erasmus refused to see him, both for 
fear of his loathsome diseases, and also because the beggared 
knight was sure to borrow money from him. A paper war 
consequently broke out between the two Humanists, which 
embittered Hutten's last days, and stained the memory of 
Erasmus. From Basel Ulrich dragged himself to Mulhausen; 
and when the vengeance of Erasmus drove him thence, he went 
to Zurich. There the large heart of Zwingli welcomed him; 
he helped him with money, and found him a quiet refuge with 
the pastor of the little isle of Ufnau on the Zurich lake. There 
the frail and worn-out poet, writing swift satire to the end, died 
at the end of August or beginning of September 1523 at the 
age of thirty-five. He left behind him some debts due to com- 
passionate friends; he did not even own a single book, and 
all his goods amounted to the clothes on his back, a bundle 
of letters, and that valiant pen which had fought so many 
a sharp battle, and had won for the poor knight-errant a sure 
place in the annals of literature. 

Ulrich von Hutten is one of those men of genius at whom 
propriety is shocked, and whom the mean-spirited avoid. Yet 
through his short and buffeted life he was befriended, with 
wonderful charity and patience, by the chief leaders of the 
Humanist movement. For, in spite of his irritable vanity, 
his immoral life and habits, his odious diseases, his painful 
restlessness, Hutten had much in him that strong men could 
love. He passionately loved the truth, and was ever open 
to all good influences. He was a patriot, whose soul soared 
to ideal schemes and a grand Utopian restoration of his country. 
In spite of all. his was a frank and noble nature; his faults chiefly 
the faults of genius ill-controlled, and of a life cast in the eventful 
changes of an age of novelty. A swarm of writings issued from 
his pen; at first the smooth elegance of his Latin prose and verse 
seemed strangely to miss his real character; he was the Cicero 
and Ovid of Germany before he became its Lucian. 

His chief works were his Ars versificandi (1511) ; the Nemo (1518) ; 
a work on the Morbus Gallicus (1519); the volume of Steckelberg 
complaints against Duke Ulrich (including his four Ciceronian 
Orations, his Letters and the Phalarismus) also in 1519; the Vadismus 
(1520); and the controversy with Erasmus at the end of his life. 
Besides these were many admirable poems in Latin and German. 
It is not known with certainty how far Hutten was the parent of the 
celebrated Epistolae obscurorum virorum, that famous satire on 
monastic ignorance as represented by the theologians of Cologne 
with which the friends of Reuchlin defended him. At first the 
cloister-world, not discerning its irony, welcomed the work as a 
defence of their position; though their eyes were soon opened by 
the favour with which the learned world received it. The Epistolae 
were eagerly bought up; the first part (41 letters) appeared at the 
end of 1515; early in 1516 there was a second edition; later in 1516 
a third, with an appendix of seven letters; in 1517 appeared the 
second part (62 letters), to which a fresh appendix of eight letters 
was subjoined soon after. In 1909 the Latin text of the Epistolae 
with an English translation was published by F. G. Stokes. Hutten, 
in a letter addressed to Robert Crocus, denied that he was the author 
of the book, but there is no doubt as to his connexion with it. 
Erasmus was of opinion that there were three authors, of whom 
Crotus Rubianus was the originator of the idea, and Hutten a chief 
contributor. IX F. Strauss, who dedicates to the subject a chapter 
of his admirable work on Hutten, concludes that he had no share in 
the first part, but that his hand is clearly visible in the second part, 
which he attributes in the main to him. To him is due the more 
serious and severe tone of that bitter portion of the satire. See 
VV. Brecht, Die Verfasser der Epistolae obscurorum virorum (1904). 

For a complete catalogue of trie writings of Hutten, see E. Booking's 
Index bibliographicus Hullenianus (1858). Booking is also the editor 
of the complete edition of Hutten's works (7 vols., 1859-1862). A 
selection of Hutten's German writings, edited by G. Balke, appeared 
in 1891. Cp. S. Szamatolski, Hultens deutsche Schriften (1891). 
The best biography (though it is also somewhat of a political 
pamphlet) is that of D. F. Strauss (Ulrich von Hutten, 1857; 
4th ed., 1S78; English translation by G. Sturge, 1874), with 
which may be compared the older monographs by A. Wagenseil 
(1823), A. Biirck (1846) and J. Zeller (Paris, 1849). See also 
J. Deckert, Ulrich von Huttens Leben und Wirken. Eine historische 
Skizze (1901). (G. VV. K.) 

HUTTER, LEONHARD (1 563-1616), German Lutheran 
theologian, was born at Nellingen near Ulm in January 1563. 
From 1 58 1 he studied at the universities of Strassburg, Leipzig, 



Heidelberg and Jena. In 1594 he began to give theological 
lectures at Jena, and in 1596 accepted a call as professor of 
theology at Wittenberg, where he died on the 23rd of October 
1616. Hutter was a stern champion of Lutheran orthodoxy, 
as set down in the confessions and embodied in his own 
Compendium locorum theologicorum (1610; reprinted 1863), 
being so faithful to his master as to win the title of " Luther 
redonatus." 

In reply to Rudolf Hospinian's Concordia discors (1607), he wrote 
a work, rich in historical material but one-sided in its apologetics, 
Concordia concors (1614), defending the formula of Concord, which 
he regarded as inspired. His Irenicum vere christianum is directed 
against David Pareus (1548-1622), professor primariusat Heidelberg, 
who in Irenicum sive de unione et synodo Evangelicorum (1614) had 
pleaded for a reconciliation of Lutheranism and Calvinism; his 
Calvinista aulopoliticus (1610) was written against the " damnable 
Calvinism " which was becoming prevalent in Holstein and Branden- 
burg. Another work, based on the formula of Concord, was entitled 
Loci communes theologici. 

HUTTON, CHARLES (1737-1823), English mathematician, 
was born at Newcastle-on-Tyne on the 14th of August 1737. 
He was educated in a school at Jesmond, kept by Mr Ivison, 
a clergyman of the church of England. There is reason to believe, 
on the evidence of two pay-bills, that for a short time in 1755 
and 1756 Hutton worked in Old Long Benton colliery; at any 
rate, on Ivison's promotion to a living, Hutton succeeded to 
the Jesmond school, whence, in consequence of increasing pupils, 
he removed to Stote's Hall. While he taught during the day 
at Stote's Hall, he studied mathematics in the evening at a 
school in Newcastle. In 1760 he married, and began tuition 
on a larger scale in Newcastle, where he had among his pupils 
John Scott, afterwards Lord Eldon, chancellor of England. 
In 1764 he published his first work, The Schoolmaster's Guide, 
or a Complete System of Practical Arithmetic, which in 1770 
was followed by his Treatise on Mensuration both in Theory and 
Practice. In 1772 appeared a tract on The Principles of Bridges, 
suggested by the destruction of Newcastle bridge by a high 
flood on the 17th of November 1771. In 1773 he was appointed 
professor of mathematics at the Royal Military Academy, 
Woolwich, and in the following year he was elected F.R.S. and 
reported on Nevil Maskelyne's determination of the mean density 
and mass of the earth from measurements taken in 1774-1776 at 
Mount Schiehallion in Perthshire. This account appeared in the 
Philosophical Transactions for 1778, was afterwards reprinted 
in the second volume of his Tracts on Mathematical and Philo- 
sophical Subjects, and procured for Hutton the degree of LL.D. 
from the university of Edinburgh. He was elected foreign 
secretary to the Royal Society in 1779, but his resignation in 
1783 was brought about by the president Sir Joseph Banks, 
whose behaviour to the mathematical section of the society 
was somewhat high-handed (see Kippis's Observations on the 
late Contests in the Royal Society, London, 1784). After his 
Tables of the Products and Powers of Numbers, 1781, and his 
Mathematical Tables, 1785, he issued, for the use of the Royal 
Military Academy, in 1787 Elements of Conic Sections, and in 1798 
his Course of Mathematics. His Mathematical and Philosophical 
Dictionary, a valuable contribution to scientific biography, 
was published in 179s (2nd ed., 1815), and the four volumes of 
Recreations in Mathematics and Natural Philosophy, mostly a 
translation from the French, in 1803. One of the most laborious 
of his works was the abridgment, in conjunction with G. Shaw 
and R. Pearson, of the Philosophical Transactions. This under- 
taking, the mathematical and scientific parts of which fell -to 
Hutton's share, was completed in 1809, and filled eighteen 
volumes quarto. His name first appears in the Ladies' Diary 
(a poetical and mathematical almanac which was begun in 
1704, and lasted till 1871) in 1764; ten years later he was 
appointed editor of the almanac, a post which he retained till 
1817. Previously he had begun a small periodical, Miscellanea 
Mathematica, which extended only to thirteen numbers; subse- 
quently he published in five volumes The Diarian Miscellany, 
which contained large extracts from the Diary. He resigned 
his professorship in 1807, and died on the 27th of January 1823. 
See John Bruce, Charles Hutton (Newcastle, 1823). 



i6 



HUTTON, J.— BUTTON, R. H. 



HUTTON, JAMES (1726-1707), Scottish geologist, was born 
in Edinburgh on the 3rd of June 1726. Educated at the high 
school and university of his native city, he acquired while a 
student a passionate love of scientific inquiry. He was ap- 
prenticed to a lawyer, but his employer advised that a moie 
congenial profession should be chosen for him. The young 
apprentice chose medicine as being nearest akin to his favourite 
pursuit of chemistry. He studied for three years at Edinburgh, 
and completed his medical education in Paris, returning by 
the Low Countries, and taking his degree of doctor of medicine 
at Leiden in 1749. Finding, however, that there seemed hardly 
any opening for him, he abandoned the medical profession, 
and, having inherited a small property in Berwickshire from 
his father, resolved to devote himself to agriculture. He then 
went to Norfolk to learn the practical work of farming, and 
subsequently travelled in Holland, Belgium and the north 
of France. During these years he began to study the surface 
of the earth, gradually shaping in his mind the problem 
to which he afterwards devoted his energies. In the summer 
of 1754 he established himself on his own farm in Berwickshire, 
where he resided for fourteen years, and where he introduced 
the most improved forms of husbandry. As the farm was 
brought into excellent order, and as its management, becoming 
more easy, grew less interesting, he was induced to let it, and 
establish himself for the rest of his life in Edinburgh. This took 
place about the year 1768. He was unmarried, and from this 
period until his death in 1797 he lived with his three sisters. 
Surrounded by congenial literary and scientific friends he 
devoted himself to research. 

At that time geology in any proper sense of the term did 

not exist. Mineralogy, however, had made considerable progress. 

But Hutton had conceived larger ideas than were entertained 

by the mineralogists of his day. He desired to trace back the 

origin of the various minerals and rocks, and thus to arrive 

at some clear understanding of the history of the earth. For 

many years he continued to study the subject. At last, in the 

spring of the year 1785, he communicated his views to the 

recently established Royal Society of Edinburgh in a paper 

entitled Theory of the Earth, or an Investigation of the Laws 

Observable in the Composition, Dissolution and Restoration of 

Land upon the Globe. In this remarkable work the doctrine 

is expounded that geology is not cosmogony, but must confine 

itself to the study of the materials of the earth; that everywhere 

evidence may be seen that the present rocks of the earth's 

surface have been in great part formed out of the waste of older 

rocks; that these materials having been laid down under the 

sea were there consolidated under great pressure, and were 

subsequently disrupted and upheaved by the expansive power 

of subterranean heat; that during these convulsions veins 

and masses of molten rock were injected into the rents of the 

dislocated strata; that every portion of the upraised land, 

as soon as exposed to the atmosphere, is subject to decay; and 

that this decay must tend to advance until the whole of the 

land has been worn away and laid down on the sea-floor, whence 

future upheavals will once more raise the consolidated sediments 

into new land. In some of these broad and bold generalizations 

Hutton was anticipated by the Italian geologists; but to him 

belongs the credit of having first perceived their mutual relations, 

and combined them in a luminous coherent theory based upon 

observation. 

It was not merely the earth to which Hutton directed his 
attention. He had long studied the changes of the atmosphere. 
The same volume in which his Theory of the Earth appeared 
contained also a Theory of Rain, which was read to the Royal 
Society of Edinburgh in 1784. He contended that the amount 
of moisture which the air can retain in solution increases with 
augmentation of temperature, and, therefore, that on the 
mixture of two masses of air of different temperatures a portion 
of the moisture must be condensed and appear in visible form. 
He investigated the available data regarding rainfall and climate 
in different regions of the globe, and came to the conclusion 
that the rainfall is everywhere regulated by the humidity of the 



air on the one hand, and the causes which promote mixtures 
of different aerial currents in the higher atmosphere on 
the other. 

The vigour and versatility of his genius may be understood 
from the variety of works which, during his thirty years' residence 
in Edinburgh, he gave to the world. In 1792 he published a . 
quarto volume entitled Dissertations on different Subjects in 
Natural Philosophy, in which he discussed the nature of matter, 
fluidity, cohesion, light, heat and electricity. Some of these 
subjects were further illustrated by him in papers read before 
the Royal Society of Edinburgh. He did not restrain himself 
within the domain of physics, but boldly marched into that of 
metaphysics, publishing three quarto volumes with the title 
A n Investigation of the Principles of Knowledge, and of the Progress 
of Reason — from Sense to Science and Philosophy. In this work 
he developed the idea that the external world, as conceived 
by us, is the creation of our own minds influenced by impressions 
from without, that there is no resemblance between our picture 
of the outer world and the reality, yet that the impressions 
produced upon our minds, being constant and consistent, become 
as much realities to us as if they precisely resembled things 
actually existing, and, therefore, that our moral conduct must 
remain the same as if our ideas perfectly corresponded to the 
causes producing them. His closing years were devoted to the 
extension and republication of his Theory of the Earth, of which 
two volumes appeared in 1795. A third volume, necessary 
to complete the work, was left by him in manuscript, and is 
referred to by his biographer John Playfair. A portion of the 
MS. of this volume, which had been given to the Geological 
Society of London by Leonard Horner, was published by the 
Society in 1899, under the editorship of Sir A. Geikie. The 
rest of the manuscript appears to be lost. Soon afterwards 
Hutton set to work to collect and systematize his numerous 
writings on husbandry, which he proposed to publish under 
the title of Elements of Agriculture. He had nearly completed 
this labour when an incurable disease brought his active career 
to a close on the 26th of March 1797. 

It is by his Theory of the Earth that Hutton will be remembered 
with reverence while geology continues to be cultivated. The 
author's style, however, being somewhat heavy and obscure, the 
book did not attract during his lifetime so much attention as it de- 
served. Happily for science Hutton numbered among his friends 
John Playfair (q.v.), professor of mathematics in the university of 
Edinburgh, whose enthusiasm for the spread of Hutton's doctrine 
was combined with a rare gift of graceful and luminous exposition. 
Five years after Hutton's death he published a volume, Illustrations 
of the Huttonian Theory of the Earth, in which he gave an admirable 
summary of that theory, with numerous additional illustrations and 
arguments. This work is justly regarded as one of the classical con- 
tributions to geological literature. To its influence much of the 
sound progress of British geology must be ascribed. In the year 
1805 a biographical account of Hutton, written by Playfair, was 
published in vol. v. of the Transactions of the Royal Society of Edin- 
burgh. (A. Ge.) 

HUTTON, RICHARD HOLT (1826-1897), English writer 
and theologian, son of Joseph Hutton, Unitarian minister at 
Leeds, was born at Leeds on the 2nd of June 1826. His family 
removed to London in 1835, and he was educated at University 
College School and University College, where he began a lifelong 
friendship with Walter Bagehot, of whose works he afterwards 
was the editor; he took the degree in 1845, being awarded the 
gold medal for philosophy. Meanwhile he had also studied 
for short periods at Heidelberg and Berlin, and in 1847 ne entered 
Manchester New College with the idea of becoming a minister 
like his father, and studied there under James Martinealu 
He did not, however, succeed in obtaining a call to any church, 
and for some little time his future was unsettled. He married 
in 1851 his cousin, Anne Roscoe, and became joint-editor with 
J. L. Sanford of the Inquirer, the principal Unitarian organ. 
But his innovations and his unconventional views about stereo- 
typed Unitarian doctrines caused alarm, and in 1853 he resigned. 
His health had broken down, and he visited the West Indies, 
where his wife died of yellow fever. In 1855 Hutton and Bagehot 
became joint-editors of the National Review, a new monthly, 
and conducted it for ten years. During this time Hutton's 
theological views, influenced largely by Coleridge, and more 



HUXLEY 



r 7 



directly by F. W. Robertson and F. D. Maurice, gradually 
approached more and more to those of the Church of England, 
which he ultimately joined. His interest in theology was 
profound, and he brought to it a spirituality of outlook and 
an aptitude for metaphysical inquiry and exposition which 
added a singular attraction to his writings. In 1861 he joined 
Meredith Townsend as joint-editor and part proprietor of the 
Spectator, then a well-known liberal weekly, which, however, 
was not remunerative from the business point of view. Hutton 
took charge of the literary side of the paper, and by degrees 
his own articles became and remained up to the last one of the 
best-known features of serious and thoughtful English journalism. 
The Spectator, which gradually became a prosperous property, 
was his pulpit, in which unwearyingly he gave expression to 
his views, particularly on literary, religious and philosophical 
subjects, in opposition to the agnostic and rationalistic opinions 
then current in intellectual circles, as popularized by Huxley. 
A man of fearless honesty, quick and catholic sympathies, broad 
culture, and many friends in intellectual and religious circles, 
he became one of the most influential journalists of the day, 
his fine character and conscience earning universal respect and 
confidence. He was an original member of the Metaphysical 
Society (1869). He was an anti-vivisectionist, and a member 
of the royal commission (1875) on that subject. In 1858 he 
had married Eliza Roscoe, a cousin of his first wife; she died 
early in 1897, and Hutton's own death followed on the 9th of 
September of the same year. 

Among his other publications may be mentioned Essays, Theo- 
logical and Literary (1871; revised 1888), and Criticisms on Con- 
temporary Thought and Thinkers (1894); and his opinions may be 
studied compendiously in the selections from his Spectator articles 
published in 1899 under the title of Aspects of Religious and Scientific 
Thought. 

HUXLEY, THOMAS HENRY (1825-1895), English biologist, 
was born on the 4th of May 1825 at Ealing, where his father, 
George Huxley, was senior assistant-master in the school of 
Dr Nicholas. This was an establishment of repute, and is at 
any rate remarkable for having produced two men with so 
little in common in after life as Huxley and Cardinal Newman. 
The cardinal's brother, Francis William, had been " captain " 
of the school in 1821. Huxley was a seventh child (as his father 
had also been), and the youngest who survived infancy. Of 
Huxley's ancestry no more is ascertainable than in the case 
of most middle-class families. He himself thought it sprang 
from the Cheshire Huxleys of Huxley Hall. Different branches 
migrated south, one, now extinct, reaching London, where its 
members were apparently engaged in commerce. They estab- 
lished themselves for four generations at Wyre Hall, near 
Edmonton, and one was knighted by Charles II. Huxley describes 
his paternal race as " mainly Iberian mongrels, with a good 
dash of Norman and a little Saxon." 1 From his father he thought 
he derived little except a quick temper and the artistic faculty 
which proved of great service to him and reappeared in an even 
more striking degree in his daughter, the Hon. Mrs Collier. 
" Mentally and physically," he wrote, " I am a piece of my 
mother." Her maiden name was Rachel Withers. " She came 
of Wiltshire people," he adds, and describes her as " a typical 
example of the Iberian variety." He tells us that " her most 
distinguishing characteristic was rapidity of thought. . . That 
peculiarity has been passed on to me in full strength " (Essays, i. 
4). One of the not least striking facts in Huxley's life is that 
of education in the formal sense he received none. " I had 
two years of a pandemonium of a school (between eight and 
ten), and after that neither help nor sympathy in any intellectual 
direction till I reached manhood " (Life, ii. 145). After the 
death of Dr Nicholas the Ealing school broke up, and Huxley's 
father returned about 1835 to his native town, Coventry, where 
he had obtained a small appointment. Huxley was left to 
his own devices; few histories of boyhood could offer any 
parallel. At twelve he was sitting up in bed to read Hutton's 
Geology. His great desire was to be a mechanical engineer; 
it ended in his devotion to " the mechanical engineering of living 
1 Nature, lxiii. 127. 



machines." His curiosity in this direction was nearly fatal; 
a post-mortem he was taken to between thirteen and fourteen 
was followed by an illness which seems to have been the starting- 
point of the ill-health which pursued him all through life. At 
fifteen he devoured Sir William Hamilton's Logic, and thus 
acquired the taste for metaphysics, which he cultivated to the 
end. At seventeen he came under the influence of Thomas 
Carlyle's writings. Fifty years later he wrote: " To make 
things clear and get rid of cant and shows of all sorts. This 
was the lesson I learnt from Carlyle's books when I was a boy, 
and it has stuck by me all my life " (Life, ii. 268). Incidentally 
they led him to begin to learn German; he had already acquired 
French., At seventeen Huxley, with his elder brother James, 
commenced regular medical studies at Charing Cross Hospital, 
where they had both obtained scholarships. He studied under 
Wharton Jones, a physiologist who never seems to have attained 
the reputation he deserved. Huxley said of him: "I do not 
know that I ever felt so much respect for a teacher before or 
since " (Life, i. 20). At twenty he passed his first M.B. examina- 
tion at the University of London, winning the gold medal for 
anatomy and physiology; W. H. Ransom, the well-known 
Nottingham physician, obtaining the exhibition. In 1845 ■ 
he published, at the suggestion of Wharton Jones, his first 
scientific paper, demonstrating the existence of a hitherto 
unrecognized layer in the inner sheath of hairs, a layer that 
has been known since as " Huxley's layer." 

Something had to be done for a livelihood, and at the sugges- 
tion of a fellow-student, Mr (afterwards Sir Joseph) Fayrer, he 
applied for an appointment in the navy. He passed the necessary 
examination, and at the same time obtained the qualification of 
the Royal College of Surgeons. He was " entered on the books 
of Nelson's old ship, the ' Victory,' for duty at Haslar Hospital." 
Its chief, Sir John Richardson, who was a well-known Arctic 
explorer and naturalist, recognized Huxley's ability, and pro- 
cured for him the post of surgeon to H.M.S. " Rattlesnake," 
about to start for surveying work in Torres Strait. The com- 
mander, Captain Owen Stanley, was a son of the bishop of 
Norwich and brother of Dean Stanley, and wished for an officer 
with some scientific knowledge. Besides Huxley the " Rattle- 
snake " also carried a naturalist by profession, John Macgillivray, 
who, however, beyond a dull narrative of the expedition, ac- 
complished nothing. The " Rattlesnake " left England on the 
3rd of December 1846, and was ordered home after the lamented 
death of Captain Stanley at Sydney, to be paid off at Chatham 
on the gth of November 1850. The tropical seas teem with 
delicate surface-life, and to the study of this Huxley devoted 
himself with unremitting devotion. At that time no known 
methods existed by which it could be preserved for study in 
museums at home. He gathered a magnificent harvest in 
the almost unreaped field, and the conclusions he drew from 
it were the beginning of the revolution in zoological science 
which he lived to see accomplished. 

Baron Cuvier (1769-1832), whose classification still held 
its ground, had divided the animal kingdom into four great 
embranchements. Each of these corresponded to an independent 
archetype, of which the "idea" had existed in the mind of 
the Creator. There was no other connexion between these 
classes, and the " ideas " which animated them were, as far 
as one can see, arbitrary. Cuvier's groups, without their 
theoretical basis, were accepted by K. E. von Baer (1792-1876). 
The " idea " of the group, or archetype, admitted of endless 
variation within it; but this was subordinate to essential 
conformity with the archetype, and hence Cuvier deduced the 
important principle of the " correlation of parts," of which 
he made such conspicuous use in palaeontological reconstruction. 
Meanwhile the " Naturphilosophen," with J. W. Goethe (1740- 
1832) and L. Oken (1770-1851), had in effect grasped the under- 
lying principle of correlation, and so far anticipated evolution 
by asserting the possibility of deriving specialized from simpler 
structures. Though they were still hampered by idealistic 
conceptions, they established morphology. Cuvier's four great 
groups were Vertebrata, Mollusca, Articulata and Radiata. 



i8 



HUXLEY 



It was amongst the members of the last class that Huxley found 
most material ready to his hand in the seas of the tropics. It 
included organisms of the most varied kind, with nothing more 
in common than that their parts were more or less distributed 
round a centre. Huxley sent home " communication after 
communication to the Linnean Society," then a somewhat 
somnolent body, " with the same result as that obtained by 
Noah when he sent the raven out of the ark " (Essays, i. 13). 
His important paper, On the Anatomy and the Affinities of the 
Family of Medusae, met with a better fate. It was communicated 
by the bishop of Norwich to the Royal Society, and printed 
by it in the Philosophical Transactions in 1849. Huxley 
united, with the Medusae, the Hydroid and Sertularian polyps, 
to form a class to which he subsequently gave the name of 
Hydrozoa. This alone was no inconsiderable feat for a young 
surgeon who had only had the training of the medical school. 
But the ground on which it was done has led to far-reaching 
theoretical developments. Huxley realized that something 
more than superficial characters were necessary in determining 
the affinities of animal organisms. He found that all the members 
of the class consisted of two membranes enclosing a central 
cavity or stomach. This is characteristic of what are now 
called the Coelenterata. All animals higher than these have 
been termed Coelomata; they possess a distinct body-cavity 
in addition to the stomach. Huxley went further than this, 
and the most profound suggestion in his paper is the comparison 
of the two layers with those which appear in the germ of the 
higher animals. The consequences which have flowed from 
this prophetic generalization of the ectoderm and endoderm are 
familiar to every student of evolution. The conclusion was 
the more remarkable as at the time he was not merely free 
from any evolutionary belief, but actually rejected it. The 
value of Huxley's work was immediately recognized. On 
returning to England in 1850 he was elected a Fellow of the Royal 
Society. In the following year, at the age of twenty-six, he not 
merely received the Royal medal, but was elected on the council. 
With absolutely no aid from any one he had placed himself 
in the front rank of English scientific men. He secured the 
friendship of Sir J. D. Hooker and John Tyndall, who remained 
his lifelong friends. The Admiralty retained him as a nominal 
assistant-surgeon, in order that he might work up the observations 
he had made during the voyage of the " Rattlesnake." He was 
thus enabled to produce various important memoirs, especially 
those on certain Ascidians, in which he solved the problem 
of Appendicularia — an organism whose place in the animal 
kingdom Johannes Miiller had found himself wholly unable 
to assign — and on the morphology of the Cephalous Mollusca. 

Richard Owen, then the leading comparative anatomist in 
Great Britain, was a disciple of Cuvier, and adopted largely from 
him the deductive explanation of anatomical fact from idealistic 
conceptions. He superadded the evolutionary theories of 
Oken, which were equally idealistic, but were altogether re- 
pugnant to Cuvier. Huxley would have none of either. Imbued 
with the methods of von Baer and Johannes Miiller, his methods 
were purely inductive. He would not hazard any statement 
beyond what the facts revealed. He retained, however, as has 
been done by his successors, the use of archetypes, though they 
no longer represented fundamental " ideas " but generalizations 
of the essential points of structure common to the individuals 
of each class. He had not wholly freed himself, however, from 
archetypal trammels. " The doctrine," he says, " that every 
natural group is organized after a definite archetype . . . seems 
to me as important for zoology as the doctrine of definite pro- 
portions for chemistry." This was in 1853. He further stated: 
" There is no progression from a lower to a higher type, but 
merely a more or less complete evolution of one type " (Phil. 
Trans., 1853, p. 63). As Chalmers Mitchell points out, this state- 
ment is of great historical interest. Huxley definitely uses the word 
" evolution," and admits its existence within the great groups. 
He had not, however, rid himself of the notion that the archetype 
was a property inherent in the group. Herbert Spencer, whose 
acquaintance he made in 1852, was unable to convert him to 



evolution in its widest sense (Life, i. 168). He could not bring 
himself to acceptance of the theory — owing, no doubt, to his 
rooted aversion from a priori reasoning — without a mechanical 
conception of its mode of operation. In his first interview 
with Darwin, which seems to have been about the same time, 
he expressed his belief " in the sharpness of the lines of demarca- 
tion between natural groups," and was received with a humorous 
smile (Life, i. 169). 

The naval medical service exists for practical purposes. It 
is not surprising, therefore, that after his three years' nominal 
employment Huxley was ordered on active service. Though 
without private means of any kind, he resigned. The navy, 
however, retains the credit of having started his scientific career 
as well as that of Hooker and Darwin. Huxley was now thrown 
on his own resources, the immediate prospects of which were 
slender enough. As a matter of fact, he had not to wait many 
months. His friend, Edward Forbes, was appointed to the chair 
of natural history in Edinburgh, and in July 1854 he succeeded 
him as lecturer at the School of Mines and as naturalist to the 
Geological Survey in the following year. The latter post he 
hesitated at first to accept, as he " did not care for fossils " 
(Essays, i. 15). In 1855 he married Miss H. A. Heathorn, whose 
acquaintance he had made in Sydney. They were engaged 
when Huxley could offer nothing but the future promise of his 
ability. The confidence of his devoted helpmate was not mis- 
placed, and her affection sustained him to the end, after she 
had seen him the recipient of every honour which English science 
could bestow. His most important research belonging to this 
period was the Croonian Lecture delivered before the Royal 
Society in 1858 on " The Theory of the Vertebrate Skull." 
In this he completely and finally demolished, by applying as 
before the inductive method, the idealistic, if in some degree 
evolutionary, views of its origin which Owen had derived from 
Goethe and Oken. This finally disposed of the " archetype," 
and may be said once for all to have liberated the English 
anatomical school from the deductive method. 

In 1859 The Origin of Species was published. This was a 
momentous event in the history of science, and not least for 
Huxley. Hitherto he had turned a deaf ear to evolution. " I 
took my stand," he says, " upon two grounds: firstly, that . . . 
the evidence in favour of transmutation was wholly insufficient; 
and secondly, that no suggestion respecting the causes of the 
transmutation assumed, which had been made, was in any 
way adequate to explain the phenomena " (Life, i. 168). Huxley 
had studied Lamarck " attentively," but to no purpose. Sir 
Charles Lyell " was the chief agent in smoothing the road for 
Darwin. For consistent uniformitarianism postulates evolution 
as much in the organic as in the inorganic world" (I.e.); and 
Huxley found in Darwin what he had failed to find in Lamarck, 
an intelligible hypothesis good enough as a working basis. Yet 
with the transparent candour which was characteristic of him, 
he never to the end of his life concealed the fact that he thought 
it wanting in rigorous proof. Darwin, however, was a naturalist; 
Huxley was not. He says: "I am afraid there is very little 
of the genuine naturalist in me. I never collected anything, 
and species- work was always a burden to me; what I cared 
for was the architectural and engineering part of the business " 
(Essays, i. 7). But the solution of the problem of organic evolu- 
tion must work upwards from the initial stages, and it is precisely 
for the study of these that " species- work " is necessary. Darwin, 
by observing the peculiarities in the distribution of the plants 
which he had collected in the Galapagos, was started on the 
path that led to his theory. Anatomical research had only 
so far led to transcendental hypothesis, though in Huxley's 
hands it had cleared the decks of that lumber. He quotes with 
approval Darwin's remark that " no one has a right to examine 
the question of species who has not minutely described many " 
(Essays, ii. 283). The rigorous proof which Huxley demanded 
was the production of species sterile to one another by selective 
breeding (Life, i. 193). But this was a misconception of the 
question. Sterility is a physiological character, and the specific 
differences which the theory undertook to account for are 



HUXLEY 



l 9 



morphological; there is no necessary nexus between the two. 
Huxley, however, felt that he had at last a secure grip of evolution. 
He warned Darwin: " I will stop at no point as long as clear 
reasoning will carry me further" {Life, i. 172). Owen, who 
had some evolutionary tendencies, was at first favourably 
disposed to Darwin's theory, and even claimed that he had to 
some extent anticipated it in his own writings. But Darwin, 
though he did not thrust it into the foreground, never flinched 
from recognizing that man could not be excluded from his theory. 
" Light will be thrown on the origin of man and his history " 
(Origin, ed. i. 488). Owen could not face the wrath of fashionable 
orthodoxy. In his Rede Lecture he endeavoured to save the 
position by asserting that man was clearly marked off from all 
other animals by the anatomical structure of his brain. This 
was actually inconsistent with known facts, and was effectually 
refuted by Huxley in various papers and lectures, summed up in 
1 863 in Man's Place in Nature. This " monkey damnification " of 
mankind was too much even for the " veracity " of Carlyle, who 
is said to have never forgiven it. Huxley had not the smallest 
respect for authority as a basis for belief, scientific or other- 
wise. He held that scientific men were morally bound " to try all 
things and hold fast to that which is good " (Life, ii. 161). Called 
upon in 1862, in the absence of the president, to deliver the presi- 
dential address to the Geological Society, he disposed once for all 
of one of the principles accepted by geologists, that similar fossils 
in distinct regions indicated that the strata containing them 
were contemporary. All that could be concluded, he pointed 
out, was that the general order of succession was the same. 
In 1854 Huxley had refused the post of palaeontologist to the 
Geological Survey; but the fossils for which he then said that 
he " did not care " soon acquired importance in his eyes, as 
supplying evidence for the support of the evolutionary theory. 
The thirty-one years during which he occupied the chair of 
natural history at the School of Mines were largely occupied 
with palaeontological research. Numerous memoirs on fossil 
fishes established many far-reaching morphological facts. The 
study of fossil reptiles led to his demonstrating, in the course 
of lectures on birds, delivered at the College of Surgeons in 1867, 
the fundamental affinity of the two groups which he united 
under the title of Sauropsida. An incidental result of the same 
course was his proposed rearrangement of the zoological regions 
into which P. L. Sclater had divided the world in 1857. Huxley 
anticipated, to a large extent, the results at which botanists have 
since arrived: he proposed as primary divisions, Arctogaea — 
to include the land areas of the northern hemisphere — and 
Notogaea for the remainder. Successive waves of life originated 
in and spread from the northern area, the survivors of the more 
ancient types finding successively a refuge in the south. Though 
Huxley had accepted the Darwinian theory as a working 
hypothesis, he never succeeded in firmly grasping it in detail. 
He thought " evolution might conceivably have taken place 
without the development of groups possessing the characters 
of species " (Essays, v. 41). His palaeontological researches 
ultimately led him to dispense with Darwin. In 1892 he wrote: 
" The doctrine of evolution is no speculation, but a generalization 
of certain facts . . . classed by biologists under the heads 
of Embryology and of Palaeontology " (Essays, v. 42). Earlier 
in 1 88 1 he had asserted even more emphatically that if the 
hypothesis of evolution " had not existed, the palaeontologist 
would have had to invent it " (Essays, iv. 44). 

From 1870 onwards he was more and more drawn away from 
scientific research by the claims of public duty. Some men 
yield the more readily to such demands, as their fulfilment 
is not unaccompanied by public esteem. But he felt, as he 
himself said of Joseph Priestley, " that he was a man and a 
citizen before he was a philosopher, and that the duties of the 
two former positions are at least as imperative as those of the 
latter " (Essays, iii. 13). From 1862 to 1884 he served on no 
less than ten Royal Commissions, dealing in every case with 
subjects of great importance, and in many with matters of the 
gravest moment to the community. He held and filled with 
invariable dignity and distinction more public positions than 



have perhaps ever fallen to the lot of a scientific man in England. 
From 1871 to 1880 he was a secretary of the Royal Society. 
From 1881 to 1885 he was president. For honours he cared 
little, though they were within his reach; it is said that he 
might have received a peerage. He accepted, however, in 1892, 
a Privy Councillorship, at once the most democratic and the 
most aristocratic honour accessible to an English citizen. In 
1870 he was president of the British Association at Liverpool, and 
in the same year was elected a member of the newly constituted 
London School Board. He resigned the latter position in 
1872, but in the brief period during which he acted, probably 
more than any man, he left his mark on the foundations of 
national elementary education. He made war on the scholastic 
methods which wearied the mind in merely taxing the memory; 
the children were to be prepared to take their place worthily 
in the community. Physical training was the basis; domestic 
economy, at any rate for girls, was insisted upon, and for all 
some development of the aesthetic sense by means of drawing 
and singing. Reading, writing and arithmetic were the in- 
dispensable tools for acquiring knowledge, and intellectual 
discipline was to be gained through the rudiments of physical 
science. He insisted on the teaching of the Bible partly as a great 
literary heritage, partly because he was " seriously perplexed 
to know by what practical measures the religious feeling, which 
is the essential basis of conduct, was to be kept up, in the present 
utterly chaotic state of opinion in these matters, without its 
use " (Essays, iii. 397). In 1872 the School of Mines was moved 
to South Kensington, and Huxley had, for the first time after 
eighteen years, those appliances for teaching beyond the 
lecture room, which to the lasting injury of the interests of 
biological science in Great Britain had been withheld from 
him by the short-sightedness of government. Huxley had 
only been able to bring his influence to bear upon his pupils 
by oral teaching, and had had no opportunity by personal 
intercourse in the laboratory of forming a school. He was now 
able to organize a system of instruction for classes of elementary 
teachers in the general principles of biology, which indirectly 
affected the teaching of the subject throughout the country. 

The first symptoms of physical failure to meet the strain of 
the scientific and public duties demanded of him made some 
rest imperative, and he took a long holiday in Egypt. He still 
continued for some years to occupy himself mainly with verte- 
brate morphology. But he seemed to find more interest and the 
necessary mental stimulus to exertion in lectures, public addresses 
and more or less controversial writings. His health, which 
had for a time been fairly restored, completely broke down 
again in 1885. In 1890 he removed from London to East- 
bourne, where after a painful illness he died on the 29th of 
June 1895. 

The latter years of Huxley's life were mainly occupied with con- 
tributions to periodical literature on subjects connected with philo- 
sophy and theology. The effect produced by these on popular 
opinion was profound. This was partly due to his position as a 
man of science, partly to his obvious earnestness and sincerity, but 
in the main to his strenuous and attractive method of exposition. 
Such studies were not wholly new to him, as they had more or less 
engaged his thoughts from his earliest days. That his views exhibit 
some process of development and are not wholly consistent was, 
therefore, to be expected, and for this reason it is not easy to 
summarize them as a connected body of teaching. They may be 
found perhaps in their most systematic form in the volume on Hume 
published in 1879. 

Huxley's general attitude to the problems of theology and 
philosophy was technically that of scepticism. " I am," he wrote, 
" too much of a sceptic to deny the possibility of anything " (Life-, iL 
127). " Doubt is a beneficent demon " (Essays, ix. 56). He was 
anxious, nevertheless, to avoid the accusation of Pyrrhonism (Life, ii. 
280), but the Agnosticism which he defined to express his position 
in 1869 suggests the Pyrrhonist Aphasia. The only approach to 
certainty which he admitted lay in the order of nature. "The 
conception of the constancy of the order of nature has become the 
dominant idea of modern thought. . . . Whatever may be man's 
speculative doctrines, it is quite certain that every intelligent person 
guides his life and risks his fortune upon the belief that the order of 
nature is constant, and that the chain of natural causation is never 
broken." He adds, however, that "it by no means necessarily 
follows that we are justified in expanding this generalization into the 
infinite past " (Essays, iv. 47, 48). This was little more than a pious 



20 



HUY 



reservation, as evolution implies the principle of continuity (I.e. p. 55). 
Later he stated his belief even more absolutely: " If there is any- 
thing in the world which I do firmly believe in, it is the universal 
validity of the law of causation, but that universality cannot be 
proved by any amount of experience " (Essays, ix. 121). The 
assertion that " There is only one method by which intellectual truth 
can be reached, whether the subject-matter of investigation belongs 
to the world of physics or to the world of consciousness " (Essays, ix. 
126) laid him open to the charge of materialism, which he vigorously 
repelled. His defence, when he rested it on the imperfection of the 
physical analysis of matter and force (I.e. p. 131), was irrelevant; he 
was- on sounder ground when he contended with Berkeley " that our 
certain knowledge does not extend beyond our states of conscious- 
ness " (I.e. p. 130). " Legitimate materialism, that is, the extension 
of the conceptions and of the methods of physical science to the 
highest as well as to the lowest phenomena of vitality, is neither 
more nor less than a sort of shorthand idealism " (Essays, i. 194). 
While " the substance of matter is a metaphysical unknown quality 
of the existence of which there is no proof . . . the non-existence of 
a substance of mind is equally arguable ; . . . the result ... is the 
reduction of the All to co-existences and sequences of phenomena 
beneath and beyond which there is nothing cognoscible " (Essays, ix. 
66). Hume had defined a miracle as a " violation of the laws of 
nature." Huxley refused to accept this. While, on the one hand, he 
insists that " the whole fabric of practical life is built upon our 
faith in its continuity " (Hume, p. 129), on the other " nobody 
can presume to say what the order of nature must be " ; this " knocks 
the bottom out of all a priori objections either to ordinary 'miracles' 
or to the efficacy of prayer " (Essays, v. 133). " If by the term 
miracles we mean only extremely wonderful events, there can be no 
just ground for denying the possibility of their occurrence " (Hume, 
p. 134). Assuming the chemical elements to be aggregates of uniform 
primitive matter, he saw no more theoretical difficulty in water 
being turned into alcohol in the miracle at Cana, than in sugar 
undergoing a similar conversion (Essays, v. 81). The credibility of 
miracles with Huxley is a question of evidence. It may be remarked 
that a scientific explanation is destructive of the supernatural 
character of a miracle, and that the demand for evidence may be 
so framed as to preclude the credibility of any historical event. 
Throughout his life theology had a strong attraction, not without 
elements of repulsion, for Huxley. The circumstances of his early 
training, when Paley was the " most interesting Sunday reading 
allowed him when a boy " (Life, ii. 57), probably had something to 
do with both. In i860 his beliefs were apparently theistic: " Science 
seems to me to teach in the highest and strongest manner the 
great truth which is embodied in the Christian conception of entire 
surrender to the will of God " (Life, i. 219). In 1885 he formulates 
" the perfect ideal of religion " in a passage which has become 
almost famous: " In the 8th century B.C. in the heart of a world of 
idolatrous polytheists, the Hebrew prophets put forth a conception 
of religion which appears to be as wonderful an inspiration of genius 
as the art of Pheidias or the science of Aristotle. ' And what doth 
the Lord require of thee, but to do justly, and to love mercy, and to 
walk numbly with thy God ' " (Essays, iv. 161). Two years later he 
was writing: " That there is no evidence of the existence of such a 
being as the God of the theologians is true enough " (Life, ii. 162). 
He insisted, however, that " atheism is on purely philosophical 
grounds untenable " (I.e.). His theism never really advanced 
beyond the recognition of " the passionless impersonality of the 
unknown and unknowable, which science shows everywhere under- 
lying the thin veil of phenomena " (Life, i. 239 ) ; In other respects 
his personal creed was a kind of scientific Calvinism. There is an 
interesting passage in an essay written in 1892, "An Apologetic 
Eirenicon/' which has not been republished, which illustrates this: 
" It is the secret of the superiority of the best theological teachers to 
the majority of their opponents that they substantially recognize 
these realities of things, however strange the forms in which they 
clothe their conceptions. The doctrines of predestination, of original 
sin, of the innate depravity of man and the evil fate of the greater 
part of the race, of the primacy of Satan in this world, of the essential 
vileness of matter, of a malevolent Demiurgus subordinate to a 
benevolent Almighty, who has only lately revealed himself, faulty 
as they are, appear to me to be vastly nearer the truth than the 
' liberal ' popular illusions that babies are all born good, and that the 
example of a corrupt society is responsible for their failure to remain 
so ; that it is given to everybody to reach the ethical ideal if he will 
only try; that all partial evil is universal good, and other optimistic 
figments, such as that which represents ' Providence ' under the 
guise of a paternal philanthropist, and bids us believe that everything 
will come right (according to our notions) at last." But his " slender 
definite creed," R. H. Hutton, who was associated with him in 
the Metaphysical Society, thought — and no doubt rightly — in no 
respect " represented the cravings of his larger nature.' 

From 1880 onwards till the very end of his life, Huxley was 
continuously occupied in a controversial campaign against orthodox 
beliefs. As Professor W. F. R. Weldon justly said of his earlier 
polemics: "They were certainly among the principal agents in 
winning a larger measure of toleration for the critical examination of 
fundamental beliefs, and for the free expression of honest reverent 
doubt." He threw Christianity overboard bodily and with little 



appreciation of its historic effect as a civilizing agency. He thought 
that " the exact nature of the teachings and the convictions of 
Jesus is extremely uncertain " (Essays, v. 348). " What we are 
usually pleased to call religion nowadays is, for the most part, 
Hellenized Judaism " (Essays, iv. 162). His final analysis of what 
" since the second century, has assumed to itself the title of Orthodox 
Christianity " is a " varying compound of some of the best and 
some of the worst elements of Paganism and Judaism, moulded in 
practice by the innate character of certain people of the Western 
world " (Essays, v. 142). He concludes " That this Christianity is 
doomed to fall is, to my mind, beyond a doubt; but its fall will 
neither be sudden nor speedy " (I.e.). He did not omit, however, 
to do justice to " the bright side of Christianity," and was deeply 
impressed with the life of Catherine of Siena. Failing Christianity, 
he thought that some other " hypostasis of men's hopes " will arise 
(Essays, v. 254). His latest speculations on ethical problems are 
perhaps the least satisfactory of his writings. In 1892 he wrote: 
" The moral sense is a very complex affair — dependent in part upon 
associations of pleasure and pain, approbation and disapprobation, 
formed by education in early youth, but in part also on an innate 
sense of moral beauty and ugliness (how originated need not be dis- 
cussed), which is possessed by some people in great strength, while 
some are totally devoid of it ' (Life, ii. 305). This is an intuitional 
theory, and he compares the moral with the aesthetic sense, which he 
repeatedly declares to be intuitive; thus: "All the understanding 
in the world will neither increase nor diminish the force of the 
intuition that this is beautiful and this is ugly " (Essays, ix. 80). In 
the Romanes Lecture delivered in 1894, in which this passage occurs, 
he defines " law and morals " to be " restraints upon the struggle 
for existence between men in society." It follows that " the ethical 
process is in opposition to the cosmic process," to which the struggle 
for existence belongs (Essays, ix. 31). Apparently he thought that 
the moral sense in its origin was intuitional and in its development 
utilitarian. " Morality commenced with society " (Essays, v. 52). 
The " ethical process ' is the " gradual strengthening of the social 
bond " (Essays, ix. 35). " The cosmic process has no sort of relation 
to moral ends " (I.e. p. 83) ; " of moral purpose I see no trace in 
nature. That is an article of exclusive human manufacture " (Life, 
ii. 268). The cosmic process Huxley identified with evil, and the 
ethical process with good; the two are in necessary conflict. " The 
reality at the bottom of the doctrine of original sin " is the " innate 
tendency to self-assertion " inherited by man from the cosmic order 
(Essays, ix. 27). " The actions we call sinful are part and parcel of 
the struggle for existence " (Life, ii. 282). " The prospect of attaining 
untroubled happiness " is " an illusion " (Essays, ix. 44), and the 
cosmic process in the long run will get the best of the contest, and 
" resume its sway " when evolution enters on its downward course 
(I.e. p. 45). This approaches pure pessimism, and though in Huxley's 
view the " pessimism of Schopenhauer is a nightmare " (Essays, ix. 
200), his own philosophy of life is not distinguishable, and is often 
expressed in the same language. The cosmic order is obviously 
non-moral (Essays, ix. 197). That it is, as has been said, immoral 
is really meaningless. Pain and suffering are affections which 
imply a complex nervous organization, and we are not justified in 
projecting them into nature external to ourselves. Darwin and A. R. 
Wallace disagreed with Huxley in seeing rather the joyous than the 
suffering side of nature. Nor can it be assumed that the descending 
scale of evolution will reproduce the ascent, or that man will ever be 
conscious of his doom. 

As has been said, Huxley never thoroughly grasped the Darwinian 
principle. He thought " transmutation may take place without 
transition " '(Life, i. 173). In other words, that evolution is ac- 
complished by leaps and not by the accumulation of small variations. 
He recognized the " struggle for existence " but not the gradual 
adjustment of the organism to its environment which is implied in 
" natural selection." In highly civilized societies he thought that the 
former was at an end (Essays, ix. 36) and had been replaced by the 
" struggle for enjoyment " (I.e. p. 40). But a consideration of the 
stationary population of France might have shown him that the 
effect in the one case may be as restrictive as in the other. So far 
from natural selection being in abeyance under modern social 
conditions, " it is," as Professor Karl Pearson points out, " some- 
thing we run up against at once, almost as soon as we examine a 
mortality table " (Biometrika, i. 76). The inevitable conclusion, 
whether we like it or not, is that the future evolution of humanity is 
as much a part of the cosmic process as its past history, and Huxley's 
attempt to shut the door on it cannot be maintained scientifically." , 
Authorities. — Life and Letters of Thomas Henry Huxley, by his 
son Leonard Huxley (2 vols., 1900); Scientific Memoirs of T. H. 
Huxley (4 vols., 1898-1901); Collected Essays by T. H. Huxley 
(9 vols., 1898) ; Thomas Henry Huxley, a Sketch of his Life and Work, 
by P. Chalmers Mitchell, M.A. (Oxon., 1900); a critical study 
founded on careful research and of great value. (W. T. T.-D.) 

HUY (Lat. Hoium, and Flem. Hoey), a town of Belgium, 
on the right bank of the Meuse, at the point where it is joined 
by the Hoyoux. Pop. (1Q04), 14,164. It is 19 m. E. of Namur 
and a trifle less west of Liege. Huy certainly dates from the 
7th ce^'ury, and, according to some, was founded by the emperor 



HUYGENS, C. 



21 



Antoninus in a.d. 148. Its situation is striking, with its grey 
citadel crowning a grey rock, and the fine collegiate church 
(with a 13th-century gateway) of Notre Dame built against it. 
The citadel is now used partly as a depot of military equipment 
and partly as a prison. The ruins are still shown of the abbey 
of Neumoustier founded by Peter the Hermit on his return 
from the first crusade. He was buried there in 1115, and a 
statue was erected to his memory in the abbey grounds in 
1858. Neumoustier was one of seventeen abbeys in this town 
alone dependent on the bishopric of Liege. Huy is surrounded 
by vineyards, and the bridge which crosses the Meuse at this 
point connects the fertile Hesbaye north of the river with the 
rocky and barren Condroz south of it. 

HUYGENS, CHRISTIAAN (1620-1695), Dutch mathematician, 
mechanician, astronomer and physicist, was born at the Hague 
on the 14th of April 1629. He was the second son of Sir 
Constantijn Huygens. From his father he received the rudiments 
of his education, which was continued at Leiden under A. Vinnius 
and F. van Schooten, and completed in the juridical school 
of Breda. His mathematical bent, however, soon diverted 
him from legal studies, and the perusal of some of his earliest 
theorems enabled Descartes to predict his future greatness. In 
1649 he accompanied the mission of Henry, count of Nassau, 
to Denmark, and in 1651 entered the lists of science as an assailant 
of the unsound system of quadratures adopted by Gregory of 
St Vincent. This first essay (Exetasis quadraturae circuit, 
Leiden, 1651) was quickly succeeded by his Theoremala de 
quadratura hyperboles, ellipsis, et circuli; while, in a treatise 
entitled De circuli magnitudine inventa, he made, three years 
later, the closest approximation so far obtained to the ratio 
of the circumference to the diameter of a circle. 

Another class of subjects was now to engage his attention. 
The improvement of the telescope was justly regarded as a 
sine qua non for the advancement of astronomical knowledge. 
But the difficulties interposed by spherical and chromatic 
aberration had arrested progress in that direction until, in 1655, 
Huygens, working with his brother Constantijn, hit upon a 
new method of grinding and polishing lenses. The immediate 
results of the clearer definition obtained were the detection 
of a satellite to Saturn (the sixth in order of distance from its 
primary), and the resolution into their true form of the abnormal 
appendages to that planet. Each discovery in turn was, according 
to the prevailing custom, announced to the learned world under 
the veil of an anagram — removed, in the case of the first, by the 
publication, early in 1656, of the little tract De Salurni luna 
observatio nova; but retained, as regards the second, until 
1659, when in the Sy sterna Saturnium the varying appearances 
of the so-called " triple planet " were clearly explained as the 
phases of a ring inclined at an angle of 28 to the ecliptic. Huygens 
was also in 1656 the first effective observer of the Orion nebula; 
he delineated the bright region still known by his name, and 
detected the multiple character of its nuclear star. His applica- 
tion of the pendulum to regulate the movement of clocks sprang 
from his experience of the need for an exact measure of time 
in observing the heavens. The invention dates from 1656; 
on the 16th of June 1657 Huygens presented his first " pendulum- 
clock " to the states-general; and the Horologium, containing 
a description of the requisite mechanism, was published in 
1658. 

His reputation now became cosmopolitan. As early as 1655 
the university of Angers had distinguished him with an honorary 
degree of doctor of laws. In 1663, on the occasion of his second 
visit to England, he was elected a fellow of the Royal Society, 
and imparted to that body in January 1669 a clear and concise 
statement of the laws governing the collision of elastic bodies. 
Although these conclusions were arrived at independently, and, 
as it would seem, several years previous to their publication, 
they were in great measure anticipated by the communications 
on the same subject of John Wallis and Christopher Wren, 
aiade respectively in November and December 1668. 

Huygens had before this time fixed his abode in France. 
In 1665 Colbert made to him on behalf of Louis XIV. an offer 



too tempting to be refused, and between the following year and 
1681 his residence in the philosophic seclusion of the Bibliotheque 
du Roi was only interrupted by two short visits to his native 
country. His magnum opus dates from this period. The 
Horologium oscillalorium, published with a dedication to his 
royal patron in 1673, contained original discoveries sufficient 
to have furnished materials for half a dozen striking disquisitions. 
His solution of the celebrated problem of the "centre of oscilla- 
tion " formed in itself an important event in the history of 
mechanics. Assuming as an axiom that the centre of gravity 
of any number of interdependent bodies cannot rise higher 
than the point from which it fell, he arrived, by anticipating 
in the particular case the general principle of the conservation 
of vis viva, at correct although not strictly demonstrated con- 
clusions. His treatment of the subject was the first successful 
attempt to deal with the dynamics of a system. The determina- 
tion of the true relation between the length of a pendulum 
and the time of its oscillation; the invention of the theory of 
evolutes; the discovery, hence ensuing, that the cycloid is 
its own evolute, and is strictly isochronous; the ingenious 
although practically inoperative idea of correcting the " circular 
error " of the pendulum by applying cycloidal cheeks to clocks — 
were all contained in this remarkable treatise. The theorems 
on the composition of forces in circular motion with which it 
concluded formed the true prelude to Newton's Principia, and 
would alone suffice to establish the claim of Huygens to the 
highest rank among mechanical inventors. 

In 1 68 1 he finally severed his French connexions, and returned 
to Holland. The harsher measures which about that time 
began to be adopted towards his co-religionists in France are 
usually assigned as the motive of this step. He now devoted 
himself during six years to the production of lenses of enormous 
focal distance, which, mounted on high poles, and connected with 
the eye-piece by means of a cord, formed what were called " aerial 
telescopes." Three of his object-glasses, of respectively 123, 
180 and 210 ft. focallength, are in the possession of the Royal 
Society. He also succeeded in constructing an almost perfectly 
achromatic eye-piece, still known by his name. But his re- 
searches in physical optics constitute his chief title-deed to 
immortality. Although Robert Hooke in 1668 and Ignace 
Pardies in 1672 had adopted a vibratory hypothesis of light, 
the conception was a mere floating possibility until Huygens 
provided it with a sure foundation. His powerful scientific 
imagination enabled him to realize that all the points of a wave- 
front originate partial waves, the aggregate effect of which is 
to reconstitute the primary disturbance at the subsequent stages 
of its advance, thus accomplishing its propagation; so that 
each primary undulation is the envelope of an indefinite number 
of secondary undulations. This resolution of the original wave 
is the well-known " Principle of Huygens," and by its means 
he was enabled to prove the fundamental laws of optics, and 
to assign the correct construction for the direction of the extra- 
ordinary ray in uniaxial crystals. These investigations, together 
with his discovery of the " wonderful phenomenon " of polariza- 
tion, are recorded in his Traite de la lumiere, published at 
Leiden in 1690, but composed in 1678. In the appended 
treatise Sur la Cause de la pesanteur, he rejected gravitation as 
a universal quality of matter, although admitting the Newtonian 
theory of the planetary revolutions. From his views on centri- 
fugal force he deduced the oblate figure of the earth, estimating 
its compression, however, at little more than one-half its actual 
amount. 

Huygens never married. He died at the Hague on the 8th 
of June 1695, bequeathing his manuscripts to the university 
of Leiden, and his considerable property to the sons of his 
younger brother. In character he was as estimable as he was 
brilliant in intellect. Although, like most men of strong originative 
power, he assimilated with difficulty the ideas of others, his 
tardiness sprang rather from inability to depart from the track 
of his own methods than from reluctance to acknowledge the 
merits of his competitors. 

In addition to the works already mentioned, his Cosmotheoros — 



22 



HUYGENS, SIR C— HUYSMANS 



a speculation concerning the inhabitants of the planets— was printed 
posthumously at the Hague in 1698, and appeared almost simultane- 
ously in an English translation. A volume entitled Opera posthuma 
(Leiden, 1703) contained his " Dioptrica," in which the ratio between 
the respective focal lengths of object-glass and eye-glass is given as 
the measure of magnifying power, together with the shorter essays 
De yitris figurandis, De corona et parheliis, &c. An early tract De 
ratiociniis in ludo aleae, printed in 1657 with Schooten's Exercita- 
tiones mathematicae, is notable as one of the first formal treatises on 
the theory of probabilities; nor should his investigations of the 
properties of the cissoid, logarithmic and catenary curves be left 
unnoticed. His invention of the spiral watch-spring was explained 
m the Journal des savants (Feb. 25, 1675). An edition of his 
works was published by G. J. 's Gravesande, in four quarto volumes 
entitled Opera varia (Leiden, 1724) and Opera reliqua (Amsterdam, 
1728). His scientific correspondence was edited by P. J. Uylenbroek 
from manuscripts preserved at Leiden, with the title Christiani 
Hugenii aliommque seculi X VII. virorum cclebrium exercitationes 
mathematicae et philosophicae (the Hague, 1833). 

The publication of a monumental edition of the letters and works 
of Huygens was undertaken at the Hague by the Society Hollandaise 
des Sciences, with the heading CEuvres de Christian Huygens (1888), 
&c. Ten quarto volumes, comprising the whole of his correspondence, 
had already been issued in 1905. A biography of Huygens was 
prefixed to his Opera varia (1724); his Eloge in the character of a 
French academician was printed by J. A. N. Condorcet in 1773. 
Consult further: P. J. Uylenbroek, Oratio de fratribus Chrisliano 
atque Constantino Hugenio (Groningen, 1838) ; P. Harting, Christiaan 
Huygens in zijn Leven en Werken geschetzt (Groningen, 1868) ; J. B. J. 
Delambre, Hist, de I'astronomie moderne (ii. 549) ; J. E. Montucla, 
Hist, des mathematiques (ii. 84, 412, 549); M. Chasles, Apercu histor- 
ique sur I'origine des methodes en geometrie, pp. 101-109; E. Diihring, 
Kritische Geschichte der allgemeinen Principien der Mechanik, 
Abschnitt (ii. 120, 163, iii. 227); A. Berry, A Short History of 
Astronomy, p. 200; R. Wolf, Geschichte der Asironomie, passim; 
Houzeau, Bibliographic astronomique (ii. 169) ; F. Kaiser, Astr. Nach. 
(xxv. 245, 1847); Tijdschrift voor de Wetenschappen (i. 7, 1848); 
Allgemeine deutsche Biographie (M. B. Cantor) ; J. C. Poggendorff, 
Biog. lit. Handworterbuch. (A. M. C.) 

HUYGENS, SIR CONSTANTIJN (1596-1687), Dutch poet 
and diplomatist, was born at the Hague on the 4th of September 
1596. His father, Christiaan Huygens, was secretary to the 
state council, and a man of great political importance. At the 
baptism of the child, the city of Breda was one of his sponsors, 
and the admiral Justinus van Nassau the other. He was trained 
in every polite accomplishment, and before he was seven could 
speak French with fluency. He was taught Latin by Johannes 
Dedelus, and soon became a master of classic versification. 
He developed not only extraordinary intellectual gifts but 
great physical beauty and strength, and was one of the most 
accomplished athletes and gymnasts of his age; his skill in 
playing the lute and in the arts of painting and engraving 
attracted general attention before he began to develop his 
genius as a writer. In 1616 he proceeded, with his elder brother, 
to the university of Leiden. He stayed there only one year, 
and in 1618 went to London with the English ambassador 
Dudley Carleton; he remained in London for some months, 
and then went to Oxford, where he studied for some time in the 
Bodleian Library, and to Woodstock, Windsor and Cambridge; 
he was introduced at the English court, and played the lute 
before James I. The most interesting feature of this visit was 
the intimacy which sprang up between the young Dutch poet 
and Dr Donne, for whose genius Huygens preserved through 
life an unbounded admiration. He returned to Holland in 
company with the English contingent of the synod of Dort, 
and in 16 19 he proceeded to Venice in the diplomatic service 
of his country; on his return he nearly lost his life by a foolhardy 
exploit, namely, the scaling of the topmost spire of Strassburg 
cathedral. In 162 1 he published one of his most weighty and 
popular poems, his Batava Tempe, and in the same year he 
proceeded again to London, as secretary to the ambassador, 
Wijngaerdan, but returned in three months. His third diplo- 
matic visit to England lasted longer, from the 5th of December 
1621 to the 1st of March 1623. During his absence, his volume 
of satires, '/ Costelick Mai, dedicated to Jacob Cats, appeared 
at the Hague. In the autumn of 1622 he was knighted by 
James I. He published a large volume of miscellaneous poems 
in 1625 under the title of Otiorum libri sex; and in the same 
year he was appointed private secretary to the stadholder. 



In 1627 Huygens married Susanna van Baerle, and settled at 
the Hague; four sons and a daughter were born to them. In 
1630 Huygens was called to a seat in the privy council, and he 
continued to exercise political power with wisdom and vigour 
for many years, under the title of the lord of Zuylichem. In 
1634 he is supposed to have completed his long-talked-of version 
of the poems of Donne, fragments of which exist. In 1637 his 
wife died,- and he immediately began to celebrate the virtues 
and pleasures of their married life in the remarkable didactic 
poem called Dagwerck, which was not published till long after- 
wards. From 1639 to 1641 he occupied himself by building 
a magnificent house and garden outside the Hague, and by 
celebrating their beauties in a poem entitled Hofwijck, which 
was published in 1653. In 1647 he wrote his beautiful poem 
of Oogentroost or " Eye Consolation," to gratify his blind friend 
Lucretia van Trollo. He made his solitary effort in the dramatic 
line in 1657, when he brought out his comedy of Trijntje Cornells 
Klachl, Which deals, in rather broad humour, with the adventures 
of the wife of a ship's captain at Zaandam. In 1658 he rearranged 
his poems, and issued them with many additions, under the 
title of Corn Flowers. He proposed to the government that 
the present highway from the Hague to the sea at Scheveningen 
should be constructed, and during his absence on a diplomatic 
mission to the French court in 1666 the road was made as a 
compliment to the venerable statesman, who expressed his 
gratitude in a descriptive poem entitled Zeestraet. Huygens 
edited his poems for the last time in 1672, and died in his ninety- 
first year, on the 28th of March 1687. He was buried, with the 
pomp of a national funeral, in the church of St Jacob, on the 
4th of April. His second son, Christiaan, the eminent astronomer, 
is noticed separately. 

Constantijn Huygens is the most brilliant figure in Dutch literary 
history. Other statesmen surpassed him in political influence, and 
at least two other poets surpassed him in the value and originality of 
their writings. But his figure was more dignified and, splendid, his 
talents were more varied, and his general accomplishments more 
remarkable than those of any other person of his age, the greatest 
age in the history of the Netherlands. Huygens is the grand seigneur 
of the republic, the type of aristocratic oligarchy, the jewel and 
ornament of Dutch liberty. When we consider his imposing character 
and the positive value of his writings, we may well be surprised that 
he has not found a modern editor. It is a disgrace to Dutch scholar- 
ship that no complete collection of the writings of Huygens exists. 
His autobiography, De vita propria sermonum libri duo, did not see 
the light until 1817, and his remarkable poem, Chiyswerck, was not 
printed until 1841. As a poet Huygens shows a finer sense of form 
than any other early Dutch writer; the language, in his hands, 
becomes as flexible as Italian. His epistles and lighter pieces, in par- 
ticular, display his metrical ease and facility to perfection. (E. G.) 

HUYSMANS, the name of four Flemish painters who matricu- 
lated in the Antwerp gild in the 17th century. Cornelis the 
elder, apprenticed in 1633, passed for a mastership in 1636, 
and remained obscure. Jacob, apprenticed to Frans Wouters 
in 1650, wandered to England towards the close of the reign 
of Charles II., and competed with Lely as a fashionable portrait 
painter. He executed a portrait of the queen, Catherine of 
Braganza, now in the national portrait gallery, and Horace 
Walpole assigns to him the likeness of Lady Bellasys, catalogued 
at Hampton Court as a work of Lely. His portrait of Izaak 
Walton in the National Gallery shows a disposition to imitate 
the styles of Rubens and Van Dyke. According to most accounts 
he died in London in 1696. Jan Baptist Huysmans, born at 
Antwerp in 1654, matriculated in 1676-1677, and died there in 
1715-1716- He was younger brother to Cornelis Huysmans 
the second, who was born at Antwerp in 1648, and educated 
by Gaspar de Wit and Jacob van Artois. Of Jan Baptist little 
or nothing has been preserved, except that he registered numerous 
apprentices at Antwerp, and painted a landscape dated 1697 
now in the Brussels museum. Cornelis the second is the only 
master of the name of Huysmans whose talent was largely 
acknowledged. He received lessons from two artists, one of 
whom was familiar with the Roman art of the Poussins, whilst 
the other inherited the scenic style of the school of Rubens. 
He combined the two in a rich, highly coloured, and usually 
effective style, which, however, was not free from monotony. 



HUYSMANS, J. K.— HWANG HO 



23 



Seldom attempting anything but woodside views with fancy 
backgrounds, half Italian, half Flemish, he painted with great 
facility, and left numerous examples behind. At the outset 
of his career he practised at Malines, where he married in 1682, 
and there too he entered into some business connexion with 
van der Meulen, for whom he painted some backgrounds. 
In 1706 he withdrew to Antwerp, where he resided till 1717, 
returning then to Malines, where he died on the 1st of June 
1727. 

Though most of his pictures were composed for cabinets rather than 
churches, he sometimes emulated van Artois in the production of 
large sacred pieces, and for many years his " Christ on the Road to 
Emmaus " adorned the choir of Notre Dame of Malines. In the 
gallery of Nantes, where three of his small landscapes are preserved, 
there hangs an " Investment of Luxembourg," by van der Meulen, of 
which he is known to have laid in the background. The national 
galleries of London and Edinburgh contain each one example of his 
skill. Blenheim, too, and other private galleries in England, possess 
one or more of his pictures. But most of his works are on the 
European continent. 

HUYSMANS, JORIS KARL (1848-1007), French novelist, 
was born at Paris on the 5th of February 1848. He belonged 
to a family of artists of Dutch extraction; he entered the 
ministry of the interior, and was pensioned after thirty years' 
service. His earliest venture in literature, Le Drageoir a Spices 
(1874), contained stories and short prose poems showing the 
influence of Baudelaire. Marthe (1876), the life of a courtesan, 
was published in Brussels, and Huysmans contributed a story, 
" Sac au dos," to Les Soirees de Midan, the collection of stories 
of the Franco-German war published by Zola. He then pro- 
duced a series of novels of everyday life, including Les Sosurs 
Vatard (1879), En Menage ( 1 88 1 ) , and ^ vau-l'eau ( 1 88 2) , in which 
he outdid Zola in minute and uncompromising realism. He 
was influenced, however, more directly by Flaubert and the 
brothers de Goncourt than by Zola. In L' Art moderne (1883) 
he gave a careful study of impressionism and in Certains (1889) 
a series of studies of contemporary artists. .4 Rebours (1884), 
the history of the morbid tastes of a decadent aristocrat, des 
Esseintes, created a literary sensation, its caricature of literary 
and artistic symbolism covering much of the real beliefs of the 
leaders of the aesthetic revolt. In Ld-Bas Huysmans's most 
characteristic hero, Durtal, makes his appearance. Durtal 
is occupied in writing the life of Gilles de Rais; the insight 
he gains into Satanism is supplemented by modern Parisian 
students of the black art; but already there are signs of a 
leaning to religion in the sympathetic figures of the religious 
bell-ringer of Saint Sulpice and his wife. En Route (1895) relates 
the strange conversion of Durtal to mysticism and Catholicism 
in his retreat to La Trappe. In La Cathedrale (1898), Huysmans's 
symbolistic interpretation of the cathedral of Chartres, he 
develops his enthusiasm for the purity of Catholic ritual. The 
life of Sainte Lydwine de Schiedam (1901), an exposition of 
the value of suffering, gives further proof of his conversion; 
and L'Oblat (1903) describes Durtal's retreat to the Val des 
Saints, where he is attached as an oblate to a Benedictine 
monastery. Huysmans was nominated by Edmond de Gon- 
court as a member of the Academie des Goncourt. He died 
as a devout Catholic, after a long illness of cancer in the palate 
on the 13th of May 1907. Before his death he destroyed his 
unpublished MSS. His last book was Les Foules de Lourdes 
(1906). 

See Arthur Symons, Studies in two Literatures (1897) and The 
Symbolist Movement in Literature (1899); Jean Lionnet in VEvolu- 
tion des idees (1903); Eugene Gilbert in France et Belgique (1905); 
J. Sargeret in Les Grands convertis (1906). 

HUYSUM, JAN VAN (1682-1749), Dutch painter, was born 
at Amsterdam in 1682, and died in his native city on the 8th 
of February 1749. He was the son of Justus van Huysum, 
who is said to have been expeditious in decorating doorways, 
screens and vases. A picture by this artist is preserved in 
the gallery of Brunswick, representing Orpheus and the Beasts 
in a wooded landscape, and here we have some explanation 
of his son's fondness for landscapes of a conventional and Arcadian 
kind; for Jan van Huysum, though skilled as a painter of still 
life, believed himself to possess the genius of a landscape painter. 



Half his pictures in public galleries are landscapes, views of 
imaginary lakes and harbours with impossible ruins and classic 
edifices, and woods of tall and motionless trees — the whole 
very glossy and smooth, and entirely lifeless. The earliest dated 
work of this kind is that of 1717, in the Louvre, a grove with 
maidens culling flowers near a tomb, ruins of a portico, and a 
distant palace on the shores of a lake bounded by mountains. 
It is doubtful whether any artist ever surpassed van Huysum 
in representing fruit and flowers. It has been said that his 
fruit has no savour and his flowers have no perfume — in other 
words, that they are hard and artificial — but this is scarcely 
true. In substance fruit and flower are delicate and finished 
imitations of nature in its more subtle varieties of matter. 
The fruit has an incomparable blush of down, the flowers have 
a perfect delicacy of tissue. Van Huysum, too, shows supreme 
art in relieving flowers of various colours against each other, 
and often against a light and transparent background. He 
is always bright, sometimes even gaudy. Great taste and 
much grace and elegance are apparent in the arrangement of 
bouquets and fruit in vases adorned with bas reliefs or in baskets 
on marble tables. There is exquisite and faultless finish every- 
where. But what van Huysum has not is the breadth, the 
bold effectiveness, and the depth of thought of de Heem, from 
whom he descends through Abraham Mignon. 

Some of the finest of van Huysum's fruit and flower pieces have 
been in English private collections: those of 1723 in the earl of 
Ellesmere's gallery, others of 1730-1732 in the collections of Hope 
and Ashburton. One of the best examples is now in the National 
Gallery (1736-1737). No public museum has finer and more numer- 
ous specimens than the Louvre, which boasts of four landscapes and 
six panels with still life; then come Berlin and Amsterdam with four 
fruit and flower pieces; then St Petersburg, Munich, Hanover, 
Dresden, the Hague, Brunswick, Vienna, Carlsruhe and Copenhagen. 
HWANG HO [Hoang Ho], the second largest river in China. 
It is known to foreigners as the Yellow river — a name which 
is a literal translation of the Chinese. It rises among the Kuen- 
lun mountains in central Asia, its head-waters being in close 
proximity to those of the Yangtsze-Kiang. It has a total 
length of about 2400 m. and drains an area of approximately 
400,000 sq. m. The main stream has its source in two lakes 
named Tsaring-nor and Oring-nor, lying about 35 N., 97 E., 
and after flowing with a south-easterly course it bends sharply 
to the north-west and north, entering China in the province 
of Kansuh in lat. 36 . After passing Lanchow-fu, the capital 
of this province, the river takes an immense sweep to the north 
and north-east, until it encounters the rugged barrier ranges 
that here run north and south through the provinces of Shansi 
and Chihli. By these ranges it is forced due south for 500 m., 
forming the boundary between the provinces of Shansi and 
Shensi, until it finds an outlet eastwards at Tung Kwan — a 
pass which for centuries has been renowned as the gate of Asia, 
being indeed the sole commercial passage between central 
China and the West. At Tung Kwan the river is joined by its 
only considerable affluent in China proper, the Wei (Wei-ho), 
which drains the large province of Shensi, and the combined 
volume of water continues its way at first east and then north- 
east across the great plain to the sea. At low water in the winter 
season the discharge is only about 36,000 cub. ft. per second, 
whereas during the summer flood it reaches 116,000 ft. or more. 
The amount of sediment carried down is very large, though 
no accurate observations have been made. In the account 
of Lord Macartney's embassy, which crossed the Yellow river 
in 1792, it was calculated to be 17,520 million cub. ft. a year, 
but this is considered very much over the mark. Two reasoift, 
however, combine to render it probable that the sedimentary 
matter is very large in proportion to the volume of water: 
the first being the great fall, and the consequently rapid current 
over two-thirds of the river's course; the second that the 
drainage area is nearly all covered with deposits of loess, which, 
being very friable, readily gives way before the rainfall and 
is washed down in large quantity. The ubiquity of this loess 
or yellow earth, as the Chinese call it, has in fact given its 
name both to the river which carries it in solution and to the 
sea (the Yellow Sea) into which it is discharged. It is calculated 



2 4 



HWICCE— HYACINTH 



by Dr Guppy {Journal of China Branch of Royal Asiatic Society, 
vol. xvi.) that the sediment brought down by the three northern 
rivers of China, viz., the Yangtsze, the Hwang-ho and the 
Peiho, is 24,000 million cub. ft. per annum, and is sufficient 
to fill up the whole of the Yellow Sea and the Gulf of Pechili 
in the space of about 36,000 years. 

Unlike the Yangtsze, the Hwang-ho is of no practical value for 
navigation. The silt and sand form banks and bars at the mouth, 
the water is too shallow in winter and the current is too strong in 
summer, and, further, the bed of the river is continually shifting. 
It is this last feature which has earned for the river the name " China's 
sorrow." As the silt-laden waters debouch from the rocky bed of the 
upper reaches on to the plains, the current slackens, and the coarser 
detritus settles on the bottom. By degrees the bed rises, and the 
people build embankments to prevent the river from overflowing. 
As the bed rises the embankments must be raised too, until the stream 
is flowing many feet above the level of the surrounding country. 
As time goes on the situation becomes more and more dangerous; 
finally, a breach occurs, and the whole river pours over the country, 
carrying destruction and ruin with it. If the breach cannot be re- 
paired the river leaves its old channel entirely and finds a new exit 
to the sea along the line of least resistance. Such in brief has been 
the story of the river since the dawn of Chinese history. At various 
times it has discharged its waters alternately on one side or the other 
of the great mass of mountains forming the promontory of Shantung, 
and by mouths as far apart from each other as 500 m. At each 
change it has worked havoc and disaster by covering the cultivated 
fields with 2 or 3 ft. of sand and mud. 

A great change in the river's course occurred in 1851, when a 
breach was made in the north embankment near Kaifengfu in Honan. 
At this point the river bed was some 25 ft. above the plain; the 
water consequently forsook the old channel entirely and poured over 
the level country, finally seizing on the bed of a small river called 
the Tsing, and thereby finding an exit to the sea. Since that time 
the new channel thus carved out has remained the proper course of 
the river, the old or southerly channel being left quite dry. It re- 
quired some fifteen or more years to repair damages from this out- 
break, and to confine the stream by new embankments. After that 
there was for a time comparative immunity from inundations, but 
in 1882 fresh outbursts again began. The most serious of all took 
place in 1887, when it appeared probable that there would be again a 
permanent change in the river's course. By dint of great exertions, 
however, the government succeeded in closing the breach, though 
not till January 1889, and not until there had been immense destruc- 
tion of life and property. The outbreak on this occasion occurred, as 
all the more serious outbreaks have done, in Honan, a few miles west 
of the city of Kaifengfu. The stream poured itself over the level and 
fertile country to the southwards, sweeping whole villages before 
it, and converting the plain into one vast lake. The area affected 
was not less than 50,000 sq. m. and the loss of life was computed at 
over one million. Since 1887 there have been a series of smaller 
outbreaks, mostly at points lower down and in the neighbourhood of 
Chinanfu, the capital of Shantung. These perpetually occurring 
disasters entail a heavy expense on the government; and from the 
mere pecuniary point of view it would well repay them to call in the 
best foreign engineering skill available, an expedient, however, which 
has not commended itself to the Chinese authorities. (G. J.) 

HWICCE, one of the kingdoms of Anglo-Saxon Britain. Its 
exact dimensions are unknown; they probably coincided with 
those of the old diocese of Worcester, the early bishops of 
which bore the title " Episcopus Hwicciorum." It would there- 
fore include Worcestershire, Gloucestershire except the Forest 
of Dean, the southern half of Warwickshire, and the neighbour- 
hood of Bath. The name Hwicce survives in Wychwood in 
Oxfordshire and Whichford in Warwickshire. These districts, 
or at all events the southern portion of them, were according 
to the Anglo-Saxon Chronicle, s.a. 577, originally conquered 
by the West Saxons under Ceawlin. In later times, however, 
the kingdom of the Hwicce appears to have been always subject 
to Mercian supremacy, and possibly it was separated from 
VVessex in the time of Edwin. The first kings of whom we read 
were two brothers, Eanhere and Eanfrith, probably contempor- 
aries of Wulfhere. They were followed by a king named Osric, 
a contemporary of iEthelred, and he by a king Oshere. Oshere 
had three sons who reigned after him, ^Ethelheard, ^Ethelweard 
and /Ethelric. The two last named appear to have been reigning 
in the year 706. At the beginning of Offa's reign we again find 
the kingdom ruled by three brothers, named Eanberht, Uhtred 
and Aldred, the two latter of whom lived until about 780. After 
them the title of king seems to have been given up. Their 
successor iEthelmund, who was killed in a campaign against 



Wessex in 802, is described only as an earl. The district re- 
mained in possession of the rulers of Mercia until the fall of that 
kingdom. Together with the rest of English Mercia it submitted 
to King Alfred about 877-883 under Earl yEthelred, who possibly 
himself belonged to the Hwicce. No genealogy or list of kings 
has been preserved, and we do not know whether the dynasty 
was connected with that of Wessex or Mercia. 

See Bede, Historia eccles. (edited by C. Plummer) iv. 13 (Oxford, 
l896);W.deG. Birch, Cartularium Saxonicum, 43, gi, 76,85 116, 117, 
122, 163, 187, 232, 233, 238 (Oxford, 1885-1889). (F. G. M. B.) 

HYACINTH (Gr. vo.ki.v6os), also called Jacinth (through Ital. 
giacinto), one of the most popular of spring garden flowers. It 
was in cultivation prior to 1597, at which date it is mentioned 
by Gerard. Rea in 1665 mentions several single and double 
varieties as being then in English gardens, and Justice in 1754 
describes upwards of fifty single-flowered varieties, and nearly 
one hundred double-flowered ones, as a selection of the best from 
the catalogues of two then celebrated Dutch growers. One of 
the Dutch sorts, called La Reine de Femmes, a single white, 
is said to have produced from thirty-four to thirty-eight flowers 
in a spike, and on its first appearance to have sold for 50 guilders 
a bulb; while one called Overwinnaar, or Conqueror, a double 
blue, sold at first for 100 guilders, Gloria Mundi for 500 guilders, 
and Koning Saloman for 600 guilders. Several sorts are at 
that date mentioned as blooming well in water-glasses. Justice 
relates that he himself raised several very valuable double- 
flowered kinds from seeds, which many of the sorts he describes 
are noted for producing freely. 

The original of the cultivated hyacinth, Hyacinthus orientalis, 
a native of Greece and Asia Minor, is by comparison an insignifi- 
cant plant, bearing on a spike only a few small, narrow-lobed, 
washy blue flowers, resembling in form those of our common 
bluebell. So great has been the improvement effected by the 
florists, and chiefly by the Dutch, that the modern hyacinth 
would scarcely be recognized as the descendant of the type above 
referred to, the spikes being long and dense, composed of a large 
number of flowers; the spikes produced by strong bulbs not 
unfrequently measure 6 to 9 in. in length and from 7 to 9 in. 
in circumference, with the flowers closely set on from bottom to 
top. Of late years much improvement has been effected in the 
size of the individual flowers and the breadth of their recurving 
lobes, as well as in securing increased brilliancy and depth of 
colour. 

The peculiarities of the soil and climate of Holland are so very 
favourable to their production that Dutch florists have made a 
specialty of the growth of those and other bulbous-rooted flowers. 
Hundreds of acres are devoted to the growth of hyacinths in the 
vicinity of Haarlem, and bring in a revenue of several hundreds 
of thousands of pounds. Some notion of the vast number 
imported into England annually may be formed from the fact 
that, for the supply of flowering plants to Covent Garden, one 
market grower alone produces from 60,000 to 70,000 in pots 
under glass, their blooming period being accelerated by artificial 
heat, and extending from Christmas onwards until they bloom 
naturally in the open ground. 

In the spring flower garden few plants make a more effective 
display than the hyacinth. Dotted in clumps in the flower 
borders, and arranged in masses of well-contrasted colours in 
beds in the flower garden, there are no flowers which impart 
during their season — March and April — a gayer tone to the par- 
terre. The bulbs are rarely grown a second time, either for 
indoor or outdoor culture, though with care they might be 
utilized for the latter purpose; and hence the enormous numbers 
which are procured each recurring year from Holland. 

The first hyacinths were single-flowered, but towards the close 
of the 17th century double-flowered ones began to appear, and 
till a recent period these bulbs were the most esteemed. At 
the present time, however, the single-flowered sorts are in the 
ascendant, as they produce more regular and symmetrical spikes 
of blossom, the flowers being closely set and more or less horizontal 
in direction, while most of the double sorts have the bells distant 
and dependent, so that the spike is loose and by comparison 



HYACINTH— HYACINTHUS 



25 



ineffective. For pot culture, and for growth in water-glasses 
especially, the single-flowered sorts are greatly to be preferred. 
Pew if any of the original kinds are now in cultivation, a succes- 
sion of new and improved varieties having been raised, the 
demand for which is regulated in some respects by fashion. 

The hyacinth delights in a rich light sandy soil. The Dutch in- 
corporate freely witu tueir naturally light soil a compost consisting 
of one-third coarse sea or river sand, one-third rotten cow dung 
without litter and one-third leaf-mould. The soil thus renovated 
retains its qualities for six or seven years, but hyacinths are not 
planted upon the same place for two years successively, intermediary 
crops of narcissus, crocus or tulips being taken. A good compost for 
hyacinths is sandy loam, decayed leaf-mould, rott-n cow dung and 
sharp sand in equal parts, the whole being collected and laid up in a 
heap and turned over occasionally. Well-drained beds made up of 
this soil, and refreshed with a portion of new compost annually, 
would grow the hyacinth to perfection. The best time to plant the 
bulbs is towards the end of September and during October; they 
should be arranged in rows, 6 to 8 in. asunder, there being four rows 
in each bed. The bulbs should be sunk about 4 to 6 in. deep, with a 
small quantity of clean sand placed below and around each of them. 
The beds should be covered with decayed tan-bark, coco-nut fibre or 
half-rotten dung litter. As the flower-stems appear, they are tied to 
rigid but slender stakes to preserve them from accident. If the bulbs 
are at all prized, the stems should be broken off as soon as the flower- 
ing is over, so as not to exhaust the bulbs; the leaves, however, must 
be allowed to grow on till matured, but as soon as they assume a 
yellow colour, the bulbs are taken up, the leaves cut off near their 
base, and the bulbs laid out in a dry, airy, shady place to ripen, after 
which they are cleaned of loose earth and skin, ready for storing. 
It is the practice in Holland, about a month after the bloom, or when 
the tips of the leaves assume a withered appearance, to take up the 
bulos, and to lay them sideways on the ground, covering them with 
an inch or two of earth. About three weeks later they are again 
taken up and cleaned. In the store-room they should be kept dry, 
well-aired and apart from each other. 

Few plants are better adapted than the hyacinth for pot culture 
as greenhouse decorative plants; and by the aid of forcing they may 
be had in bloom as early as Christmas. They flower fairly well in 
5-in. pots, the stronger bulbs in 6-in. pots. To bloom at Christmas, 
they should be potted early in September, in a compost resembling 
that already recommended for the open-air beds; and, to keep up a 
succession of bloom, others should be potted at intervals of a few 
weeks till the middle or end of November. The tops of the bulbs 
should be about level with the soil, and if a little sand is put im- 
mediately around them so much the better. The pots should be set 
in an open place on a dry hard bed of ashes, and be covered over to a 
depth of 6 or 8 in. with the same material or with fibre or soil; and 
when the roots are well developed, which will take from six to eight 
weeks, they may be removed to a frame, and gradually exposed to 
light, and then placed in a forcing pit in a heat of from 60 to 70°. 
When the flowers are fairly open, they may be removed to the green- 
house or conservatory. 

The hyacinth may be very successfully grown in glasses for orna- 
ment in dwelling-houses. The glasses are filled to the neck with rain 
or even tap water, a few lumps of charcoal being dropped into them. 
The bulbs are placed in the hollow provided for them, so that their 
base just touches the water. This may be done in September or 
October. They are then set in a dark cupboard for a few weeks till 
roots are freely produced, and then gradually exposed to light. The 
early-flowering single white Roman hyacinth, a small-growing pure 
white variety, remarkable for its fragrance, is well adapted for 
forcing, as it can be had in bloom if required by November. For 
windows it grows well in the small glasses commonly used for 
crocuses; and for decorative purposes should be planted about five 
bulbs in a 5-in. pot, or in pans holding a dozen each. If grown for 
cut flowers it can be planted thickly in boxes of any convenient size. 
It is highly esteemed during the winter months by florists. 

The Spanish hyacinth (H. amethystinus) and H. azureus are 
charming little bulbs for growing in masses in the rock garden or front 
of the flower border. The older botanists included in the genus 
Hyacinthus species of Muscari, Scilla and other genera of bulbous 
Liliaceae, and the name of hyacinth is still popularly applied to 
several other bulbous plants. Thus Muscari botryoides is the grape 
hyacinth, 6 in., blue or white, the handsomest; M. moschatum, the 
musk hyacinth, 10 in., has peculiar livid greenish-yellow flowers and 
a strong musky odour; M. comosum var. monstrosum, the feather 
hyacinth, bears sterile flowers broken up into a featherlike mass; 
M. racemosum, the starch hyacinth, is a native with deep blue plum- 
scented flowers. The Cape hyacinth is Galtonia candicans, a magnifi- 
cent border plant, 3-4 ft. high, with large drooping white bell-shaped 
flowers; the star hyacinth, Scilla amoena; the Peruvian hyacinth 
or Cuban lily, 5. peruviana, a native of the Mediterranean region, to 
which Linnaeus gave the species name peruviana on a mistaken 
assumption of its origin; the wild hyacinth or blue-bell, known 
variously as Endymion nonscriptum, Hyacinthus nonscriptus or 
Scilla nutans; the wild hyacinth of western North Amercia, Camassia 
■acidenla. They all flourish in good garden soil of a gritty nature. 



HYACINTH, or Jacinth, in mineralogy, a variety of zircon 
(q.v.) of yellowish red colour, used as a gem-stone. The hyacinthus 
of ancient writers must have been our sapphire, or blue corundum, 
while the hyacinth of modern mineralogists may have been 
the stone known as lyncurium (KvyKoV/jLOv). The Hebrew 
word leshem, translated ligure in the Authorized Version (Ex. 
xxviii. 19), from the Xtyvptov of the Septuagint, appears in 
the Revised Version as jacinth, but with a marginal alternative 
of amber. Both jacinth and amber may be reddish yellow, 
but their identification is doubtful. As our jacinth (zircon) 
is not known in ancient Egyptian work, Professor Flinders 
Petrie has suggested that the leshem may have been a yellow 
quartz, or perhaps agate. Some old English writers describe 
the jacinth as yellow, whilst others refer to it as a blue stone, 
and the hyacinthus of some authorities seems undoubtedly to 
have been our sapphire. In Rev. xx. 20 the Revised Version 
retains the word jacinth, but gives sapphire as an alternative. 

Most of the gems known in trade as hyacinth are only garnets — 
generally the deep orange-brown hessonite or cinnamon-stone — 
and many of the antique engraved stones reputed to be hyacinth 
are probably garnets. The difference may be detected optically, 
since the garnet is singly and the hyacinth doubly refracting; 
moreover the specific gravity affords a simple means of diagnosis, 
that of garnet being only about 3-7, whilst hyacinth may have 
a density as high as 4-7. Again, it was shown many years ago- 
by Sir A. H. Church that most hyacinths, when examined by 
the spectroscope, show a series of dark absorption bands, due 
perhaps to the presence of some rare element such as uranium 
or erbium. 

Hyacinth is not a common mineral. It occurs, with other 
zircons, in the gem-gravels of Ceylon, and very fine stones have 
been found as pebbles at Mudgee in New South Wales. Crystals 
of zircon, with all the typical characters of hyacinth, occur at 
Expailly, Le Puy-en-Velay, in Central France, but they are not 
large enough for cutting. The stones which have been called 
Compostella hyacinths are simply ferruginous quartz from 
Santiago de Compostella in Spain. (F. W. R.*) 

HYACINTHUS,' in Greek mythology, the youngest son of the 
Spartan king Amyclas, who reigned at Amyclae (so Pausanias 
iii. 1. 3, iii. 19. 5; and Apollodorus i. 3. 3, iii. 10. 3). Other 
stories make him son of Oebalus, of Eurotas, or of Pierus 
and the nymph Clio (see Hyginus, Fabulae, 271; Lucian, De 
saltatione, 45, and Dial. deor. 14). According to the general 
story, which is probably late and composite, his great beauty 
attracted the love of Apollo, who killed him accidentally when 
teaching him to throw the discus (quoit); others say that 
Zephyrus (or Boreas) out of jealousy deflected the quoit so that 
it hit Hyacinthus on the head and killed him. According to the 
representation on the tomb at Amyclae (Pausanias, loc. cil.) 
Hyacinthus was translated into heaven with his virgin sister 
Polyboea. Out of his blood there grew the flower known as 
the hyacinth, the petals of which were marked with the mournful 
exclamation AI, AI, " alas " (cf. " that sanguine flower inscribed 
with woe "). This Greek hyacinth cannot have been the flower 
which now bears the name : it has been identified with a species 
of iris and with the larkspur [delphinium Aiacis), which appear 
to have the markings described. The Greek hyacinth was also 
said to have sprung from the blood of Ajax. Evidently the 
Greek authorities confused both the flowers and the traditions. 

The death of Hyacinthus was celebrated at Amyclae by the 
second most important of Spartan festivals, the Hyacinthia, 
which took place in the Spartan month Hecatombeus. What 
month this was is not certain. Arguing from Xenophon (Hell. 
iv. 5) we get May; assuming that the Spartan Hecatombeus 
is the Attic Hecatombaion, we get July; or again it may be the 
Attic Scirophorion, June. At all events the Hyacinthia was an 
early summer festival. It lasted three days, and the rites 
gradually passed from mourning for Hyacinthus to rejoicings 

1 The word is probably derived from an Indo-European root, 
meaning " youthful," found in Latin, Greek, English and Sanskrit. 
Some have suggested that the first two letters are from vtw, to rain, 
(cf. Hyades). 



26 



HYADES— HYBRIDISM 



in the majesty of Apollo, the god of light and warmth, and giver 
of the ripe fruits of the earth (see a passage from Polycrates, 
Laconica, quoted by Athenaeus 139 d; criticized by L. R. 
Farnell, Cults of the Greek States, iv. 266 foil.). This festival is 
clearly connected with vegetation, and marks the passage from 
the youthful verdure of spring to the dry heat of summer and 
the ripening of the corn. 

The precise relation which Apollo bears to Hyacinthus is 
obscure. The fact that at Tarentum a Hyacinthus tomb is 
ascribed by Polybius to Apollo Hyacinthus (not Hyacinthius) 
has led some to think that the personalities are one, and that 
the hero is merely an emanation from the god; confirmation 
is sought in the Apolline appellation rerpaxeip, alleged by 
Hesychius to have been used in Laconia, and assumed to describe 
a composite figure of Apollo-Hyacinthus. Against this theory 
is the essential difference between the two figures. Hyacinthus 
is a chthonian vegetation god whose worshippers are afflicted 
and sorrowful; Apollo, though interested in vegetation, is never 
regarded as inhabiting the lower world, his death is not celebrated 
in any ritual, his worship is joyous and triumphant, and finally 
the Amyclean Apollo is specifically the god of war and song. 
Moreover, Pausanias describes the monument at Amyclae as 
consisting of a rude figure of Apollo standing on an altar-shaped 
base which formed the tomb of Hyacinthus. Into the latter 
bfferings were put for the hero before gifts were made to the god. 
On the whole it is probable that Hyacinthus belongs originally 
to the pre-Dorian period, and that his story was appropriated 
and woven into their own Apollo myth by the conquering 
Dorians. Possibly he may be the apotheosis of a pre-Dorian 
king of Amyclae. J. G. Frazer further suggests that he may 
have been regarded as spending the winter months in the under- 
world and returning to earth in the spring when the " hyacinth " 
blooms. In this case his festival represents perhaps both the 
Dorian conquest of Amyclae and the death of spring before the 
ardent heat of the summer sun, typified as usual by the discus 
(quoit) with which Apollo is said to have slain him. With the 
growth of the hyacinth from his blood should be compared the 
oriental stories of violets springing from the blood of Attis, and 
roses and anemones from that of Adonis. As a youthful vegeta- 
tion god, Hyacinthus may be compared with Linus and Scephrus, 
both of whom are connected with Apollo Agyieus. 

See L. R. Farnell, Cults of the Greek States, vol. iv. (1907), pp. 125 
foil., 264 foil.; J. G. Frazer, Adonis, Attis, Osiris (1906), bk. ii. 
ch. 7; S. Wide, Lakonische Kulte, p. 290; E. Rhode, Psyche, 
3rd ed. i. 137 foil.; Roscher, Lexikon d. griech. u. rom. Myth., s.v. 
" Hyakinthos " (Greve) ; L. Preller, Griechische Mythol. 4th ed. 
i. 248 foil. (J. M. M.) 

HYADES ("the rainy ones"), in Greek mythology, the 
daughters of Atlas and Aethra; their number varies between 
two and seven. As a reward for having brought up Zeus at 
Dodona and taken care of the infant Dionysus Hyes, whom they 
conveyed to Ino (sister of his mother Semele) at Thebes when his 
life was threatened by Lycurgus, they were translated to heaven 
and placed among the stars (Hyginus, Poet, astron. ii. 21). 
Another form of the story combines them with the Pleiades. 
According to this they were twelve (or fifteen) sisters, whose 
brother Hyas was killed by a snake while hunting in Libya 
(Ovid, Fasti, v. 165; Hyginus, Fab. 192). They lamented him 
so bitterly that Zeus, out of compassion, changed them into 
stars — five into the Hyades, at the head of the constellation 
of the Bull, the remainder into the Pleiades. Their name is 
derived from the fact that the rainy season commenced when 
they rose at the same time as the sun (May 7-21); the original 
conception of them is that of the fertilizing principle of moisture. 
The Romans derived the name from vs (pig), and translated it 
by Sucnlae (Cicero, De nat. dcorum, ii. 43). 

HYATT, ALPHEUS (1 838-1 902), American naturalist, was 
born at Washington, D.C., on the 5th of April 1838. From 
1858 to 1862 he studied at Harvard, where he had Louis Agassiz 
for his master, and in 1863 he served as a volunteer in the Civil 
War, attaining the rank of captain. In 1867 he was appointed 
curator of the Essex Institute at Salem, and in 1870 became 
professor of zoology and palaeontology at the Massachusetts 



Institute of Technology (resigned 1888), and custodian of the 
Boston Society of Natural History (curator in 1881). In 1886 
he was appointed assistant for palaeontology in the Cambridge 
museum of comparative anatomy, and in 1889 was attached 
to the United States Geological Survey as palaeontologist for 
the Trias and Jura. He was the chief founder of the American 
Society of Naturalists, of which he acted as first president in 
1883, and he also took a leading part in establishing the marine - 
biological laboratories at Annisquam and Woods Hole, Mass. 
He died at Cambridge on the 15th of January 1902. 

His works include Observations on Fresh-water Polyzoa (1866) ; 
Fossil Cephalopods of the Museum of Comparative Zoology (1872); 
Revision of North American Porifera (1875-1877); Genera of Fossil 
Cephalopoda (1883); Larval Theory of the Origin of Cellular Tissue 
(1884); Genesis of the Arietidae (1889); and Phytogeny of an ac- 
quired characteristic (1894). He wrote the section on Cephalopoda in 
Karl von Zittel's Palaontologie (1900), and his well-known study on 
the fossil pond snails of Steinheim (" The Genesis of the Tertiary 
Species of Planorbis at Steinheim ") appeared in the Memoirs of the 
Boston Natural History Society in 1880. He was one of the founders 
and editors of the American Naturalist. 

HYBLA, the name of several cities in Sicily. The best known 
historically, though its exact site is uncertain, is Hybla Major, 
near (or by some supposed to be identical with) Megara Hyblaea 
(q.v.) : another Hybla, known as Hybla Minor or Galeatis, is 
represented by the modern Paterno; while the site of Hybla 
Heraea is to be sought near Ragusa. 

HYBRIDISM. The Latin word hybrida, hibrida or ibrida 
has been assumed to be derived from the Greek fy3pis, an insult 
or outrage, and a hybrid or mongrel has been supposed to be 
an outrage on nature, an unnatural product. As a general rule 
animals and plants belonging to distinct species do not produce 
offspring when crossed with each other, and the term hybrid 
has been employed for the result of a fertile cross between 
individuals of different species, the word mongrel for the more 
common result of the crossing of distinct varieties. A closer 
scrutiny of the facts, however, makes the term hybridism less 
isolated and more vague. The words species and genus, and 
still more subspecies and variety, do not correspond with clearly 
marked and sharply defined zoological categories, and no exact 
line can be drawn between the various kinds of crossings from 
those between individuals apparently identical to those belonging 
to genera universally recognized as distinct. Hybridism therefore 
grades into mongrelism, mongrelism into cross-breeding, and cross- 
breeding into normal pairing, and we can say little more than 
that the success of the union is the more unlikely or more un- 
natural the further apart the parents are in natural affinity. 

The interest in hybridism was for a long time chiefly of a 
practical nature, and was due to the fact that hybrids are often 
found to present characters somewhat different from those of 
either parent. The leading facts have been known in the case 
of the horse and ass from time immemorial. The earliest recorded 
observation of a hybrid plant is by J. G. Gmelin towards the end 
of the 17th century; the next is that of Thomas Fairchild, who 
in the second decade of the 18th century, produced the cross 
which is still grown in gardens under the name of " Fairchild's 
Sweet William." Linnaeus made many experiments in the 
cross-fertilization of plants and produced several hybrids, but 
Joseph Gottlieb Kolreuter (1 733-1806) laid the first real founda- 
tion of our scientific knowledge of the subject. Later on Thomas 
Andrew Knight, a celebrated English horticulturist, devoted 
much successful labour to the improvement of fruit trees and 
vegetables by crossing. In the second quarter of the icpth 
century C. F. Gartner made and published the results of a number 
of experiments that had not been equalled by any earlier worker. 
Next came Charles Darwin, who first in the Origin of Species, 
and later in Cross and Self -Fertilization of Plants, subjected the 
whole question to a critical examination, reviewed the known 
facts and added many to them. 

Darwin's conclusions were summed up by G. J. Romanes in the 
9th edition of this Encyclopaedia as follows : — 

1. The laws governing the production of hybrids are identical, or 
nearly identical, in the animal and vegetable kingdoms. 

2. The sterility which so generally attends the crossing of two 
specific forms is to be distinguished as of two kinds, which, although 



HYBRIDISM 



27 



often confounded by naturalists, are in reality quite distinct. For 
the sterility may obtain between the two parent species when first 
crossed, or it may first assert itself in their hybrid progeny. In the 
latter case the hybrids, although possibly produced without any 
appearance of infertility on the part of their parent species, neverthe- 
less prove more or less infertile among themselves, and also with 
members of either parent species. 

3. The degree of both kinds of infertility varies in the case of 
different species, and in that of their hybrid progeny, from absolute 
sterility up to complete fertility. Thus, to take the case of plants, 
" when pollen from a plant of one family is placed on the stigma of a 
plant of a distinct family, it exerts no more influence than so much 
inorganic dust. From this absolute zero of fertility, the pollen of 
different species, applied to the stigma of some one species of the same 
genus, yields a perfect gradation in the number of seeds produced, up 
to nearly complete, or even quite complete, fertility; so, in hybrids 
themselves, there are some which never have produced, and probably 
never would produce, even with the pollen of the pure parents, a 
single fertile seed; but in some of these cases a first trace of fertility 
may be detected, by the pollen of one of the pure parent species 
causing the flower of the hybrid to wither earlier than it otherwise 
would have done; and the early withering of the flower is well 
known to be a sign of incipient fertilization. From this extreme 
degree of sterility we have self-fertilized hybrids producing a greater 
and greater number of seeds up to perfect fertility." 

4. Although there is, as a rule, a certain parallelism, there is no 
fixed relation between the degree of sterility manifested by the 
parent species when crossed and that which is manifested by their 
hybrid progeny. There are many cases in which two pure species 
can be crossed with unusual facility, while the resulting hybrids are 
remarkably sterile; and, contrariwise, there are species which can 
only be crossed with extreme difficulty, though the hybrids, when 
produced, are very fertile. Even within the limits of the same genus, 
these two opposite cases may occur. 

5. When two species are reciprocally crossed, i.e. male A with 
female B, and male B with female A, the degree of sterility often 
differs greatly in the two cases. The sterility of the resulting hybrids 
may differ likewise. 

6. The degree of sterility of first crosses and of hybrids runs, to a 
certain extent, parallel with the systematic affinity of the forms 
which are united. " For species belonging to distinct genera can 
rarely, and those belonging to distinct families can never, be crossed. 
The parallelism, however, is far from complete; for a multitude of 
closely allied species will not unite, or unite with extreme difficulty, 
whilst other species, widely different from each other, can be crossed 
with perfect facility. Nor does the difficulty depend on ordinary 
constitutional differences; for annual and perennial plants, decidu- 
ous and evergreen trees, plants flowering at different seasons, in- 
habiting different stations, and naturally living under the most 
opposite climates, can often be crossed with ease. The difficulty or 
facility apparently depends exclusively on the sexual constitution of 
the species which are crossed, or on their sexual elective affinity." 

There are many new records as to the production of hybrids. 
Horticulturists have been extremely active and successful in 
their attempts to produce new flowers or new varieties of vege- 
tables by seminal or graft-hybrids, and any florist's catalogue or 
the account of any special plant, such as is to be found in Foster- 
Melliar's Book of the Rose, is in great part a history of successful 
hybridization. Much special experimental work has been done 
by botanists, notably by de Vries, to the results of whose experi- 
ments we shall recur. Experiments show clearly that the 
obtaining of hybrids is in many cases merely a matter of taking 
sufficient trouble, and the successful crossing of genera is not 
infrequent. 

Focke, for instance, cites cases where hybrids were obtained 
between Brassica and Raphanus, Galium and Asperula, Campanula 
and Phyteuma, Verbascum and Celsia. Among animals, new records 
and new experiments are almost equally numerous. Boveri has 
crossed Echinus microtuberculatus with Sphaerechinus granulans. 
Thomas Hunt Morgan even obtained hybrids between Asterias, a 
starfish, and Arbacia, a sea-urchin, a cross as remote as would be 
that between a fish and a mammal. Vernon got many hybrids by 
fertilizing the eggs of Strongylocentrotus lividus with the sperm of 
Sphaerechinus granulans. Standfuss has carried on an enormous 
series of experiments with Lepidopterous insects, and has obtained a 
very large series of hybrids, of which he has kept careful record. 
Lepidopterists generally begin to suspect that many curious forms 
offered by dealers as new species are products got by crossing known 
species. Apello has succeeded with Teleostean fish; Gebhardt and 
others with Amphibia. Elliot and Suchetet have studied carefully 
the question of hybridization occurring normally among birds, and 
have got together a very large body of evidence. Among the cases 
eked by Elliot the most striking are that of the hybrid between 
Colaptes cafer and C. auratus, which occurs over a very wide area of 
North America and is known as C. hybridus, and the hybrid between 
Euplocamus lineatus and E. horsfieldi, which appears to be common in 



Assam. St M. Podmore has produced successful crosses between the 
wood-pigeon (Columba palumbus) and a domesticated variety of the 
rock pigeon (C. livia). Among mammals noteworthy results have 
been obtained by Professor Cossar Ewart, who has bred nine zebra 
hybrids by crossing mares of various sizes with a zebra stallion, and 
who has studied in addition three hybrids out of zebra mares, one 
sired by a donkey, the others by ponies. Crosses have been made 
between the common rabbit (Lepus cuniculus) and the guinea-pig 
(Cavia cobaya), and examples of the results have been exhibited in the 
Zoological Gardens of Sydney, New South Wales. The Carnivora 
generally are very easy to hybridize, and many successful experiments 
have been made with animals in captivity. Karl Hagenbeck of 
Hamburg has produced crosses between the lion (Felis leo) and the 
tiger (F. tigris). What was probably a " tri-hybrid " in which lion, 
leopard and jaguar were mingled was exhibited by a London show- 
man in 1908. Crosses between various species of the smaller cats 
have been fertile on many occasions. The black bear ( Ursus ameri- 
canus) and the European brown bear ( U. arctos) bred in the London 
Zoological Gardens in 1859, but the three cubs did not reach maturity. 
Hybrids between the brown bear and the grizzly-bear ( U. horribilis) 
have been produced in Cologne, whilst at Halle since 1874 a series of 
successful matings of polar {U. maritimus) and brown bears have 
been made. Examples of these hybrid bears have been exhibited 
by the London Zoological Society. The London Zoological Society 
has also successfully mated several species of antelopes, for instance, 
the water-bucks Kobus ellipsiprymnus and K. unctuosus, and Selous's 
antelope Limnotragus selousi with L. gratus. 

The causes militating against the production of hybrids 
have also received considerable attention. Delage, discussing 
the question, states that there is a general proportion between 
sexual attraction and zoological affinity, and in many cases 
hybrids are not naturally produced simply from absence of the 
stimulus to sexual mating, or because of preferential mating 
within the species or variety. In addition to differences of 
habit, temperament, time of maturity, and so forth, gross 
structural differences may make mating impossible. Thus 
Escherick contends that among insects the peculiar structure 
of the genital appendages makes cross-impregnation impossible, 
and there is reason to believe that the specific peculiarities 
of the modified sexual palps in male spiders have a similar 
result. 

The difficulties, however, may not exist, or may be overcome by 
experiment, and frequently it is only careful management that is 
required to produce crossing. Thus it has been found that when 
the pollen of one species does not succeed in fertilizing the ovules 
of another species, yet the reciprocal cross may be successful ; that 
is to say, the pollen of the second species may fertilize the ovules 
of the first. H. M. Vernon, working with sea-urchins, found that the 
obtaining of hybrids depended on the relative maturity of the 
sexual products. The difficulties in crossing apparently may ex- 
tend to the chemiotaxic processes of the actual sexual cells. Thus 
when the spermatozoa of an urchin were placed in a drop of sea- 
water containing ripe eggs of an urchin and of a starfish, the former 
eggs became surrounded by clusters of the male cells, while the latter 
appeared to exert little attraction for the alien germ-cells. Finally, 
when the actual impregnation of the egg is possible naturally, or has 
been secured by artificial means, the development of the hybrid may 
stop at an early stage. Thus hybrids between the urchin and the 
starfish, animals belonging to different classes, reached only the 
stage of the pluteus larva. A. D. Apello, experimenting with 
Teleostean fish, found that very often impregnation and segmenta- 
tion occurred, but that the development broke down immediately 
afterwards. W. Gebhardt, crossing Rana esculenta with R. arvalis, 
found that the cleavage of the ovum was normal, but that ab- 
normality began with the gastrula, and that development soon 
stopped. In a very general fashion there appears to be a parallel 
between the zoological affinity and the extent to which the incomplete 
development of the hybrid proceeds. 

As to the sterility of hybrids inter se, or with either of the 
parent forms, information is still wanted. Delage, summing up 
the evidence in a general way, states that mongrels are more 
fertile and stronger than their parents, while hybrids are 'at 
least equally hardy but less fertile. While many of the hybrid 
products of horticulturists are certainly infertile, others appear 
to be indefinitely fertile. 

Focke, it is true, states that the hybrids between Primula auricula 
and P. hirsuta are fertile for many generations, but not indefinitely 
so; but, while this may be true for the particular case, there seems 
no reason to doubt that many plant hybrids are quite fertile. In the 
case of animals the evidence is rather against fertility. Standfuss, 
who has made experiments lasting over many years, and who has 
dealt with many genera of Lepidoptera, obtained no fertile hybrid 
females, although he found that hybrid males paired readily and 
successfully with pure-bred females of the parent races. Elliot, 



28 



HYBRIDISM 



dealing with birds, concluded that no hybrids were fertile with one 
another beyord the second generation, but thought that they were 
fertile with -nembers of the parent races. Wallace, on the other 
hand, cites from (juatrefages tne case of hybrids between the moths 
Bombyx cynthia and B. arrindia, which were stated to be fertile 
inter se for eight generations. He also states that hybrids between 
the sheep and goat have a limited fertility inter se. Charles Darwin, 
however, had evidence that some hybrid pheasants were completely 
fertile, and he himself interbred the progeny of crosses between the 
common and Chinese geese, whilst there appears to be no doubt as to 
the complete fertility of the crosses between many species of ducks, 
J. L. Bonhote having interbred in various crosses for several genera- 
tions the mallard (Anas boschas), the Indian spot-bill duck (A. 
poecilorhyncha) , the New Zealand grey duck {A. superciliosa) and the 
pin-tail (Dafila acuta). Podmore's pigeon hybrids were fertile inter 
se, a specimen having been exhibited at the London Zoological 
Gardens. The hybrids between the brown and polar bears bred at 
Halle proved to be fertile, both with one of the parent species and 
with one another. 

Cornevin and Lesbre state that in 1873 an Arab mule was fertilized 
in Africa by a stallion, and gave birth to female offspring which she 
suckled. All three were brought to the Jardin d'Acclimatation in 
Paris, and there the mule had a second female colt to the same 
father, and subsequently two male colts in succession to an ass and 
to a stallion. The female progeny were fertilized, but their offspring 
were feeble and died at birth. Cossar Ewart gives an account of a 
recent Indian case in which a female mule gave birth to a male colt. 
He points out, however, that many mistakes have been made about 
the breeding of hybrids, and is not altogether inclined to accept this 
supposed case. Very little has been published with regard to the 
most important question, as to the actual condition of the sexual 
organs and cells in hybrids. There does not appear to be gross 
anatomical defect to account for the infertility of hybrids, but 
microscopical examination in a large number of cases is wanted. 
Cossar Ewart, to whom indeed much of the most interesting recent 
work on hybrids is due, states that in male zebra-hybrids the sexual 
cells were immature, the tails of the spermatozoa being much shorter 
than those of the similar cells in stallions and zebras. He adds, 
however, that the. male hybrids he examined were young, and might 
not have been sexually mature. He examined microscopically the 
ovary of a female zebra-hybrid and found one large and several small 
Graafian follicles, in all respects similar to those in a normal mare or 
female zebra. A careful study of the sexual organs in animal and 
plant hybrids is very much to be desired, but it may be said that so 
far as our present knowledge goes there is not to be expected any 
obvious microscopical cause of the relative infertility of hybrids. 

The relative variability of hybrids has received considerable 

attention from many writers. Horticulturists, as Bateson has 

written, are " aware of the great and striking variations which 

occur in so many orders of plants when hybridization is effected." 

The phrase has been used " breaking the constitution of a 

plant " to indicate the effect produced in the offspring of a 

hybrid union, and the device is frequently used by those who are 

seeking for novelties to introduce on the market. It may be 

said generally that hybrids are variable, and that the products 

of hybrids are still more variable. J. L. Bonhote found extreme 

variations amongst his hybrid ducks. Y. Delage states that 

in reciprocal crosses there is always a marked tendency for the 

offspring to resemble the male parents; he quotes from Huxley 

that the mule, whose male parent is an ass, is more like the ass, 

and that the hinny, whose male parent is a horse, is more like 

the horse. Standfuss found among Lepidoptera that males 

were produced much more often than females, and that these 

males paired readily. The freshly hatched larvae closely 

resembled the larvae of the female parent, but in the course of 

growth the resemblance to the male increased, the extent of the 

final approximation to the male depending on the relative 

phylogenetic age of the two parents, the parent of the older 

species being prepotent. In reciprocal pairing, he found that the 

male was able to transmit the characters of the parents in a 

higher degree. Cossar Ewart, in relation to zebra hybrids, has 

discussed the matter of resemblance to parents in very great 

detail, and fuller information must be sought in his writings. 

He shows that the wild parent is not necessarily prepotent, 

although many writers have urged that view. He described 

three hybrids bred out of a zebra mare by different horses, and 

found in all cases that the resemblance to the male or horse 

parent was more profound. Similarly, zebra-donkey hybrids 

out of zebra mares bred in France and in Australia were in 

characters and disposition far more like the donkey parents. 

The results which he obtained in the hybrids which he bred 



from a zebra stallion and different mothers were more variable, 
but there was rather a balance in favour of zebra disposition 
and against zebra shape and marking. 

" Of the nine zebra-horse hybrids I have bred," he says, " only two 
in their make and disposition take decidedly after the wild parent. 
As explained fully below, all the hybrids differ profoundly in the plan 
of their markings from the zebra, while in their ground colour they 
take after their respective dams or the ancestors of their dams far 
more than after the zebra — the hybrid out of the yellow and white 
Iceland pony, e.g. instead of being light in colour, as I anticipated, 
is for the most part of a dark dun colour, with but indistinct stripes. 
The hoofs, mane and tail of the hybrids are at the most intermediate, 
but this is perhaps partly owing to reversion towards the ancestors 
of these respective dams. In their disposition and habits they all 
undoubtedly agree more with the wild sire." 

Ewart's experiments and his discussion of them also throw 
important light on the general relation of hybrids to their 
parents. He found that the coloration and pattern of his 
zebra hybrids resembled far more those of the Somali or Grevy's 
zebra than those of their sire — a Burchell's zebra. In a general 
discussion of the stripings of horses, asses and zebras, he came 
to the conclusion that the Somali zebra represented the older 
type, and that therefore his zebra hybrids furnished important 
evidence of the effect of crossing in producing reversion to 
ancestral type. The same subject has of course been discussed 
at length by Darwin, in relation to the cross-breeding of 
varieties of pigeons; but the modern experimentalists who 
are following the work of Mendel interpret reversion differently 
(see Mendelism). 

Graft-Hybridism. — It is well known that, when two varieties or 
allied species are grafted together, each retains its distinctive 
characters. But to this general, if not universal, rule there are on 
record several alleged exceptions, in which either the scion is said 
to have partaken of the qualities of the stock, the stock of the 
scion, or each to have affected the other. Supposing any of these 
influences to have been exerted, the resulting product would 
deserve to be called a graft-hybrid. It is clearly a matter of 
great interest to ascertain whether such formation of hybrids by 
grafting is really possible; for, if even one instance of such 
formation could be unequivocally proved, it would show that 
sexual and asexual reproduction are essentially identical. 

The cases of alleged graft-hybridism are exceedingly few, con- 
sidering the enormous number of grafts that are made every year 
by horticulturists, and have been so made for centuries. Of these 
cases the most celebrated are those of Adam's laburnum (Cytisus 
Adami) and the bizzarria orange. Adam's laburnum is now 
flourishing in numerous places throughout Europe, all the trees 
having been raised as cuttings from the original graft, which was 
made by inserting a bud' of the purple laburnum into a stock of 
the yellow. M. Adam, who made the graft, has left on record 
that from it there sprang the existing hybrid. There can be no 
question as to the truly hybrid character of the latter — all the 
peculiarities of both parent species being often blended in the 
same raceme, flower or even petal; but until the experiment shall 
have been successfully repeated there must always remain a 
strong suspicion that, notwithstanding the assertion and doubt- 
less the belief of M. Adam, the hybrid arose as a cross in the 
ordinary way of seminal reproduction. Similarly, the bizzarria 
orange, which is unquestionably a hybrid between the bitter 
orange and the citron — since it presents the remarkable spectacle 
of these two different fruits blended into one — is stated by the 
gardener who first succeeded in producing it to have arisen as a 
graft-hybrid; but here again a similar doubt, similarly due to the 
need of corroboration, attaches to the statement. And the same 
remark applies to the still more wonderful case of the so-called 
trifacial orange, which blends three distinct kinds of fruit in one, 
and which is said to have been produced by artificially splitting 
and uniting the seeds taken from the three distinct species, the 
fruits of which now occur blended in the triple hybrid. 

The other instances of alleged graft-hybridism are too numer- 
ous to be here noticed in detail; they refer to jessamine, ash, 
hazel, vine, hyacinth, potato, beet and rose. Of these the cases 
of the vine, beet and rose are the strongest as evidence of graft- 
hybridization, from the fact that some of them were produced 



HYDANTOIN 



29 



as the result of careful experiments made by very competent 
experimentalists. On the whole, the results of some of these 
experiments, although so few in number, must be regarded as 
making out a strong case in favour of the possibility of graft- 
hybridism. For it must always be remembered that, in experi- 
ments of this kind, negative evidence, however great in amount, 
may be logically dissipated by a single positive result. 

Theory of Hybridism. — Charles Darwin was interested in 
hybridism as an experimental side of biology, but still more 
from the bearing of the facts on the theory of the origin of 
species. It is obvious that although hybridism is occasionally 
possible as an exception to the general infertility of species 
inter se, the exception is still more minimized when it is re- 
membered that the hybrid progeny usually display some degree 
of sterility. The main facts of hybridism appear to lend support 
to the old doctrine that there are placed between all species 
the barriers of mutual sterility. The argument for the fixity 
of species appears still stronger when the general infertility of 
species crossing is contrasted with the general fertility of the 
crossing of natural and artificial varieties. Darwin himself, 
and afterwards G. J. Romanes, showed, however, that the 
theory of natural selection did not require the possibility of the 
commingling of specific types, and that there was no reason to 
suppose that the mutation of species should depend upon their 
mutual crossing. There existed more than enough evidence, 
and this has been added to since, to show that infertility with 
other species is no criterion of a species, and that there is no 
exact parallel between the degree of affinity between forms and 
their readiness to cross. The problem of hybridism is no more 
than the explanation of the generally reduced fertility of remoter 
crosses as compared with the generally increased fertility of 
crosses between organisms slightly different. Darwin considered 
and rejected the view that the inter-sterility of species could 
have been the result of natural selection. 

" At one time it appeared to me probable," he wrote (Origin of 
Species, 6th ed. p. 247), " as it has to others, that the sterility of 
first crosses and of hybrids might have been slowly acquired through 
the natural selection of slightly lessened degrees of fertility, which, 
like any other variation, spontaneously appeared in certain indi- 
viduals of one variety when crossed with those of another variety. 
For it would clearly be advantageous to two varieties or incipient 
species if they could be kept from blending, on the same principle 
that, when man is selecting at the same time two varieties, it is 
necessary that he should keep them separate. In the first place, it 
may be remarked that species inhabiting distinct regions are often 
sterile when crossed ; now it could clearly have been of no advantage 
to such separated species to have been rendered mutually sterile and, 
consequently, this could not have been effected through natural 
selection; but it may perhaps be argued that, if a species were 
rendered sterile with some one compatriot, sterility with other 
species would follow as a necessary contingency. In the second 
place, it is almost as much opposed to the theory of natural selection 
as to that of special creation, that in reciprocal crosses the male 
element of one form should have been rendered utterly impotent on a 
second form, whilst at the same time the male element of this second 
form is enabled freely to fertilize the first form; for this peculiar 
state of the reproductive system could hardly have been advantage- 
ous to either species." 

Darwin came to the conclusion that the sterility of crossed 
species must be due to some principle quite independent of 
natural selection. In his search for such a principle he brought 
together much evidence as to the instability of the reproductive 
system, pointing out in particular how frequently wild animals 
in captivity fail to breed, whereas some domesticated races have 
been so modified by confinement as to be fertile together although 
they are descended from species probably mutually infertile. 
He was disposed to regard the phenomena of differential sterility 
as, so to speak, by-products of the process of evolution. G. J. 
Romanes afterwards developed his theory of physiological 
selection, in which he supposed that the appearance of differential 
fertility within a species was the starting-point of new species; 
certain individuals by becoming fertile only inter se proceeded 
along lines of modification diverging from the lines followed by 
other members of the species. Physiological selection in fact 
would operate in the same fashion as geographical isolation; 
if a portion of a species separated on an island tends to become 



a new species, so also a portion separated by infertility with the 
others would tend to form a new species. According to Romanes, 
therefore, mutual infertility was the starting-point, not the 
result, of specific modification. Romanes, however, did not 
associate his interesting theory with a sufficient number of facts, 
and it has left little mark on the history of the subject. A. R. 
Wallace, on the other hand, has argued that sterility between 
incipient species may have been increased by natural selection in 
the same fashion as other favourable variations are supposed to 
have been accumulated. He thought that " some slight degree 
of infertility was a not infrequent accompaniment of the external 
differences which always arise in ,a state of nature between 
varieties and incipient species." 

Weismann concluded, from an examination of a series of plant 
hybrids, that from the same cross hybrids of different character 
may be obtained, but that the characters are determined at 
the moment of fertilization; for he found that all the flowers 
on the same hybrid plant resembled one another in the minutest 
details of colour and pattern. Darwin already had pointed to the 
act of fertilization as the determining point, and it is in this 
direction that the theory of hybridism has made the greatest 
advance. 

The starting-point of the modern views comes from the 
experiments and conclusions on plant hybrids made by Gregor 
Mendel and published in 1865. It is uncertain if Darwin had 
paid attention to this work; Romanes, writing in the 9th edition 
of this Encyclopaedia, cited it without comment. First H. de 
Vries, then W. Bateson and a series of observers returned to the 
work of Mendel (see Mendelism), and made it the foundation 
of much experimental work and still more theory. It is still too 
soon to decide if the confident predictions of the Mendelians 
are justified, but it seems clear that a combination of Mendel's 
numerical results with Weismann's (see Heredity) conception 
of the particulate character of the germ-plasm, or hereditary 
material, is at the root of the phenomena of hybridism, and 
that Darwin was justified in supposing it to lie outside the 
sphere of natural selection and to be a fundamental fact of 
living matter. 

Authorities. — Apello, " tlber einige Resultate der Kreuz- 
befruchtung bei Knochenfischen," Bergens mus. aarbog (1894) ; 
Bateson, " Hybridization and Cross-breeding," Journal of the Royal 
Horticultural Society (1900); J. L. Bonhote, " Hybrid Ducks," Proc. 
Zool. Soc. of London (1905), p. 147; Boveri, article " Befruchtung," 
in Ergebnisse der Anatomie und Entwickelungsgeschichle von Merkel 
und Bonnet, i. 385-485; Cornevin et Lesbre, " jjtude sur un hybride 
issu d'une mule f&onde et d'un cheval," Rev. Set. li. 144; Charles 
Darwin, Origin of Species (1859), The Effects of Cross and Self- 
Ferlilization in the Vegetable Kingdom (1878); Delage, La Structure 
du protoplasma et les theories sur I'heredite (1895, with a literature); 
de Vries, " The Law of Disjunction of Hybrids," Comples rendus 
(1900), p. 845; Elliot, Hybridism; Escherick, " Die Diologische 
Bedeutung der Genitalabhange der Insecten," Verh. z. B. Wien, xlii. 
225; Ewart, The Ptnycuik Experiments (1899); Focke, Die 
Pflanzen-Mischlinge (1881); Foster-Melliar, The Book of the Rose 
(1894); C. F. Gaertner, various papers in Flora, 1828, 1831, 1832, 
1833, 1836, 1847, on " Bastard-Pflanzen " ; Gebhardt, "fiber die 
Bastardirung von Rana esculenla mit R. arvalis," Inaug. Dissert. 
(Breslau, 1894); G. Mendel, " Versuche iiber Pflanzen-Hybriden," 
Verh. Natur. Vereins in Briinn (1865), pp. 1-52; Morgan, " Experi- 
mental Studies," Anat. Anz. (1893), p. 141; id. p. 803; G. J. 
Romanes, " Physiological Selection," Jour. Linn. Soc. xix. 337; 
H. Scherren, Notes on Hybrid Bears," Proc. Zool. Soc. of 
London (1907), p. 431; Saunders, Proc. Roy. Soc. (1897), lxii. 11; 
Standfuss, " Etudes de zoologie experimentale," Arch. Sci. Nat. 
vi. 495; Suchetet, "Les Oiseaux hy brides rencontres a 1'iStat 
sauvage," Mim. Soc. Zool. v. 253-525, and vi. 26-45 ! Vernon, 
" The Relation between the Hybrid and Parent Forms of Echinotd 
Larvae," Proc. Roy. Soc. lxv. 350; Wallace, Darwinism (1889); 
Weismann, The Germ-Plasm (1893). (?• C. M.) 

a 

HYDANTOIN (glycolyl urea), Cj^NjOz or CO<" NH-( ? H2 . 

^NH-CO 
v 
the ureide of glycollic acid, may be obtained by heating allantoin 
or alloxan with hydriodic acid, or by heating bromacetyl urea 
with alcoholic ammonia. It crystallizes in needles, melting 
at 216 C. 
When hydrolysed with baryta water yields hydantoic 



3° 



HYDE (FAMILY)— HYDE 



(glycoluric)acid ) H 2 N'CO'NH-CH 2 -C0 2 H, which isreadily soluble 
in hot water, and on heating with hydriodic acid decomposes 
into ammonia, carbon dioxide and glycocoll, CH2-NHrC0 2 -H. 
Many substituted hydantoins are known; the a-alkyl hydantoins 
are formed on fusion of aldehyde- or ketone-cyanhydrins 
with urea, the |3-alkyl hydantoins from the fusion of mono-alkyl 
glycocolls with urea, and the 7-alkyl hydantoins from the action 
of alkalis and alkyl iodides on the a-compounds. 7-Methyl 
hydantoin has been obtained as a splitting product of caffeine 
(E. Fischer, Ann., 1882, 215, p. 253). 

HYDE, the name of an English family distinguished in the 
17th century. Robert Hyde of Norbury, Cheshire, had several 
sons, of whom the third was Lawrence Hyde of Gussage St 
Michael, Dorsetshire. Lawrence's son Henry was father of 
Edward Hyde, earl of Clarendon (q.v.), whose second son by his 
second wife was Lawrence, earl of Rochester (q.v.) ; another son 
was Sir Lawrence Hyde, attorney -general to Anne of Denmark, 
James I.'s consort; and a third son was Sir Nicholas Hyde 
(d. 1631), chief-justice of England. Sir Nicholas entered parlia- 
ment in 1601 and soon-became prominent as an opponent of the 
court, though he does not appear to have distinguished himself 
in the law. Before long, however, he deserted the popular 
party, and in 1626 he was employed by the duke of Buckingham 
in his defence to impeachment by the Commons; and in the 
following year he was appointed chief-justice of the king's bench, 
in which office it fell to him to give judgment in the celebrated 
case of Sir Thomas Darnell and others who had been committed 
to prison on warrants signed by members of the privy council, 
which contained no statement of the nature of the charge against 
the prisoners. In answer to the writ of habeas corpus the attorney- 
general relied on the prerogative of the crown, supported by 
a precedent of Queen Elizabeth's reign. Hyde, three other 
judges concurring, decided in favour of the crown, but without 
going so far as to declare the right of the crown to refuse in- 
definitely to show cause against the discharge of the prisoners. 
In 1629 Hyde was one of the judges who condemned Eliot, 
Holies and Valentine for conspiracy in parliament to resist the 
king's orders; refusing to admit their plea that they could not 
be called upon to answer out of parliament for acts done in 
parliament. Sir Nicholas Hyde died in August 1631. 

Sir Lawrence Hyde, attorney-general to Anne of Denmark, 
had eleven sons, four of whom were men of some mark. Henry 
was an ardent royalist who accompanied Charles II. to the 
continent, and returning to England was beheaded in 1650; 
Alexander (1 598-1667) became bishop of Salisbury in 1665; 
Edward (1607-1659) was a royalist divine who was nominated 
dean of Windsor in 1658, but died before taking up the appoint- 
ment, and who was the author of many controversial works in 
Anglican theology; and Robert (1595-1665) became recorder of 
Salisbury and represented that borough in the Long Parliament, 
in which he professed royalist principles, voting against the 
attainder of Strafford. Having been imprisoned and deprived 
of his recordership by the parliament in 1645/6, Robert Hyde 
gave refuge to Charles II. on his flight from Worcester in 1651, 
and on the Restoration he was knighted and made a judge of 
the common pleas. He died in 1665. Henry Hyde (1672-1753), 
only son of Lawrence, earl of Rochester, became 4th earl of 
Clarendon and 2nd earl of Rochester, both of which titles became 
extinct at his death. He was in no way distinguished, but his 
wife Jane Hyde, countess of Clarendon and Rochester (d. 1725), 
was a famous beauty celebrated by the homage of Swift, Prior and 
Pope, and by the groundless scandal of Lady Mary Wortley 
Montagu. Two of her daughters, Jane, countess of Essex, and 
Catherine, duchess of Queensberry, were also famous beauties 
of the reign of Queen Anne. Her son, Henry Hyde (1710-1753), 
known as Viscount Cornbury, was a Tory and Jacobite member 
of parliament, and an intimate friend of Bolingbroke, who 
addressed to him his Letters on the Study and Use of History, and 
On the Spirit of Patriotism. In 1750 Lord Cornbury was created 
Baron Hyde of Hindon, but, as he predeceased his father, this 
title reverted to the latter and became extinct at his death. 
Lord Cornbury was celebrated as a wit and a conversationalist. 



By his will he bequeathed the papers of his great-grandfather, 
Lord Clarendon, the historian, to the Bodleian Library at Oxford. 
See Lord Clarendon, The Life of Edward, Earl of Clarendon (3 vols., 
Oxford, 1827); Edward Foss, The Judges of England (London, 
1848-1864); Anthony a Wood, Athenae oxonienses (London, 1813- 
1820); Samuel Pepys, Diary and Correspondence, edited by Lord 
Braybrooke (4 vols., London, 1854). 

HYDE, THOMAS (1636-1703), English Orientalist, was born 
at Billingsley, near Bridgnorth, in Shropshire, on the 29th of 
June 1636. He inherited his taste for linguistic studies, and 
received his first lessons in some of the Eastern tongues, from 
his father, who was rector of the parish. In his sixteenth year 
Hyde entered King's College, Cambridge, where, under Wheelock, 
professor of Arabic, he made rapid progress in Oriental languages, 
so that, after only one year of residence, he was invited to London 
to assist Brian Walton in his edition of the Polyglott Bible. 
Besides correcting the Arabic, Persic and Syriac texts for that 
work, Hyde transcribed into Persic characters the Persian 
translation of the Pentateuch, which had been printed in Hebrew 
letters at Constantinople in 1546. To this work, which Arch- 
bishop Ussher had thought well-nigh impossible even for a 
native of Persia, Hyde appended the Latin version which accom- 
panies it in the Polyglott. In 1658 he was chosen Hebrew reader 
at Queen's College, Oxford, and in 1659, in consideration of his 
erudition in Oriental tongues, he was admitted to the degree of 
M.A. In the same year he was appointed under-keeper of the 
Bodleian Library, and in 1665 librarian-in-chief. Next year he 
was collated to a prebend at Salisbury, and in 1673 to the arch- 
deaconry of Gloucester, receiving the degree of D.D. shortly 
afterwards. In 1691 the death of Edward Pococke opened up to 
Hyde the Laudian professorship of Arabic; and in 1697, on the 
deprivation of Roger Altham, he succeeded to "the regius chair 
of Hebrew and a canonry of Christ Church. Under Charles II., 
James II. and William III. Hyde discharged the duties of 
Eastern interpreter to the court. Worn out by his unremitting 
labours, he resigned his librarianship in 1701, and died at Oxford 
on the 1 8th of February 1703. Hyde, who was one of the first 
to direct attention to the vast treasures of Oriental antiquity, 
was an excellent classical scholar, and there was hardly an Eastern 
tongue accessible to foreigners with which he was not familiar. 
He had even acquired Chinese, while his writings are the best 
testimony to his mastery of Turkish, Arabic, Syriac, Persian, 
Hebrew and Malay. 

In his chief work, Historia religionis veterum Persarum (1700), 
he made the first attempt to correct from Oriental sources the 
errors of the Greek and Roman historians who had described the 
religion of the ancient Persians. His other writings and transla- 
tions comprise Tabulae longitudinum et latitudinum stellarum 
fixarum ex observatione principis Ulugh Beighi (1665), to which 
his notes have given additional value; Quatuor evangelia et acta 
apostolorum lingua Malaica, caracteribus Europaeis (1677); 
Epislola de mensuris et ponderibus serum sive sinensium (1688), 
appended to Bernard's De mensuris et ponderibus antiquis; 
Abraham Peritsol itinera mundi (1691); and De ludis orientalibus 
libri II. (1694). 

With the exception of the Historia religionis, which was repub- 
lished by Hunt and Costard in 1760, the writings of Hyde, including 
some unpublished MSS., were collected and printed by Dr Gregory 
Sharpe in 1767 under the title Syntagma 'dissertationum quas olim. . . 
Thomas Hyde separatim edidit. There is a life of the author pre- 
fixed. Hyde also published a catalogue of the Bodleian Library 
in 1674. 

HYDE, a market town and municipal borough in the Hyde 
parliamentary division of Cheshire, England, 7^ m. E. of Man- 
chester, by the Great Central railway. Pop. (1901) 32,766. 
It lies in the densely populated district in the north-east of the 
county, on the river Tame, which here forms the boundary of 
Cheshire with Lancashire. To the east the outlying hills of the 
Peak district of Derbyshire rise abruptly. The town has cotton 
weaving factories, spinning mills, print-works, iron foundries 
and machine works; also manufactures of hats and margarine. 
There are extensive coal mines in the vicinity. Hyde is wholly 
of modern growth, though it contains a few ancient houses, such 



HYDE DE NEUVILLE— HYDERABAD 



3i 



as Newton Hall, in the part of the town so called. The old family 
of Hyde held possession of the manor as early as the reign of 
John. The borough, incorporated in 1881, is under a mayor, 
6 aldermen and 18 councillors. Area, 3081 acres. 

HYDE DE NEUVILLE, JEAN GUILLAUME, Baron (1776- 
1857), French politician, was born at La Charite-sur-Loire 
(Nievre) on the 24th of January 1776, the son of Guillaume 
Hyde, who belonged to an English family which had emigrated 
with the Stuarts after the rebellion of 1745. He was only seven- 
teen when he successfully defended a man denounced by Fouche 
before the revolutionary tribunal of Nevers. From 1 793 onwards 
he was an active agent of the exiled princes; he took part in the 
Royalist rising in Berry in 1796, and after the coup d'etat of the 
1 8th Brumaire (November 9, 1799) tried to persuade Bonaparte 
to recall the Bourbons. An accusation of complicity in the 
infernal machine conspiracy of 1800-1801 was speedily retracted, 
but Hyde de Neuville retired to the United States, only to return 
after the Restoration. He was sent by Louis XVIII. to London 
to endeavour to persuade the British government to transfer 
Napoleon to a remoter and safer place of exile than the isle of 
Elba, but the negotiations were cut short by the emperor's 
return to France in March 181 5. In January 1816 de Neuville 
became French ambassador at Washington, where he negotiated 
a commercial treaty. On his return in 182 1 he declined the 
Constantinople embassy, and in November 1822 was elected 
deputy for Cosne. Shortly afterwards he was appointed French 
ambassador at Lisbon, where his efforts to oust British influence 
culminated, in connexion with the coup d'6tat of Dom Miguel 
(April 30, 1824), in his suggestion to the Portuguese minister 
to invite the armed intervention of Great Britain. It was assumed 
that this would be refused, in view of the loudly proclaimed 
British principle of non-intervention, and that France would then 
be in a position to undertake a duty that Great Britain had 
declined. The scheme broke down, however, owing to the atti- 
tude of the reactionary party in the government of Paris, which 
disapproved of the Portuguese constitution. This destroyed 
his influence at Lisbon, and he returned to Paris to take his 
seat in the Chamber of Deputies. In spite of his pronounced 
Royalism, he now showed Liberal tendencies, opposed the 
policy of Villele's cabinet, and in 1828 became a member of the 
moderate administration of Martignac as minister of marine. 
In this capacity he showed active sympathy with the cause of 
Greek independence. During the Polignac ministry (1829- 
1830) he was again in opposition, being a firm upholder of the 
charter; but after the revolution of July 1830 he entered an 
all but solitary protest against the exclusion of the legitimate 
line of the Bourbons from the throne, and resigned his seat. 
He died in Paris on the 28th of May 1857. 

His Memoires el souvenirs (3 vols., 1888), compiled from his notes 
by his nieces, the vicomtesse de Bardonnet and the baronne Lauren- 
ceau, are of great interest for the Revolution and the Restoration. 

HYDE PARK, a small township of Norfolk county, Massa- 
chusetts, U.S.A., about 8 m. S.W. of the business centre of 
Boston. Pop. (1890) 10,193; (1900) 13,244, of whom 3805 
were foreign-born; (1910 census) 15,507. Its area is about 
45 sq. m. It is traversed by the New York, New Haven & 
Hartford railway, which has large repair shops here, and by 
the Neponset river and smaller streams. The township contains 
the villages of Hyde Park, Readville (in which there is the famous 
" Weil " trotting-track), Fairmount, Hazelwood and Clarendon 
Hills. Until about 1856 Hyde Park was a farmstead. The value 
of the total factory product increased from $4,383,959 in 1900 
to $6,739,307 in 1905, or 53-7%. In 1868 Hyde Park was 
incorporated as a township, being formed of territory taken 
from Dorchester, Dedham and Milton. 

HYDERABAD, or Haidarabad, a city and district of British 
India, in the Sind province of Bombay. The city stands on a 
hill about 3 m. from the left bank of the Indus, and Jiad a popula- 
tion in 1901 of 69,378. Upon the site of the present fort is 
supposed to have stood the ancient town of Nerankot, which 
in the 8th century submitted to Mahommed bin Kasim. In 
1768 the present city was founded by Ghulam Shah Kalhora; 



and it remained the capital of Sind until 1843, when, after the 
battle of Meeanee, it was surrendered to the British, and the 
capital transferred to Karachi. The city is built on the most 
northerly hills of the Ganga range, a site of great natural strength. 
In the fort, which covers an area of 36 acres, is the arsenal of 
the province, transferred thither from Karachi in 1861, and the 
palaces of the ex-mirs of Sind. An excellent water supply is 
derived from the Indus. In addition to manufactures of silk, 
gold and silver embroidery, lacquered ware and pottery, there 
are three factories for ginning cotton. There are three high 
schools, training colleges for masters and mistresses, a medical 
school, an agricultural school for village officials, and a technical 
school. The city suffered from plague in 1896-1897. 

The District of Hyderabad has an area of 8291 sq. m., 
with a population in 1901 of 989,030, showing an increase of 
15% in the decade. It consists of a vast alluvial plain, on the 
left bank of the Indus, 216 m. long and 48 broad. Fertile along 
the course of the river, it degenerates towards the east into 
sandy wastes, sparsely populated, and defying cultivation. The 
monotony is relieved by the fringe of forest which marks the 
course of the river, and by the avenues of trees that line the 
irrigation channels branching eastward from this stream. The 
south of the district has a special feature in its large natural 
water-courses (called dhoras) and basin-like shallows (chhaus), 
which retain the rains for a long time. A limestone range 
called the Ganga and the pleasant frequency of garden lands 
break the monotonous landscape. The principal crops are 
millets, rice, oil-seeds, cotton and wheat, which are dependent 
on irrigation, mostly from government canals. There is a special 
manufacture at Hala of glazed pottery and striped cotton cloth. 
Three railways traverse the district: (1) one of the main lines 
of the North-Western system, following the Indus valley and 
crossing the river near Hyderabad; (2) a broad-gauge branch 
running south to Badin, which will ultimately be extended 
to Bombay; and (3) a metre-gauge line from Hyderabad city 
into Rajputana. 

HYDERABAD, Haidarabad, also known as the Nizam's 
Dominions, the principal native state of India in extent, popula- 
tion and political importance; area, 82,698 sq. m.; pop. 
(1901) 11,141,142, showing a decrease of 3-4% in the decade: 
estimated revenue 45 crores of Hyderabad rupees (£2,500,000). 
The state occupies a large portion of the eastern plateau of the 
Deccan. It is bounded on the north and north-east by Berar, 
on the south and south-east by Madras, and on the west by 
Bombay. The country presents much variety of surface and 
feature; but it may be broadly divided into two tracts, dis- 
tinguished from one another geologically and ethnically, which 
are locally known from the languages spoken as Telingana and 
Marathwara. In some parts it is mountainous, wooded and 
picturesque, in others flat and undulating. The open country 
includes lands of all descriptions, including many rich and fertile 
plains, much good land not yet brought under cultivation, and 
numerous tracts too sterile ever to be cultivated. In the north- 
west the geological formations are volcanic, consisting principally 
of trap, but in some parts of basalt; in the middle, southern 
and south-western parts the country is overlaid with gneissic 
formations. The territory is well watered, rivers being numerous, 
and tanks or artificial pieces of water abundant, especially in 
Telingana. The principal rivers are the Godavari, with its 
tributaries the Dudna, Manjira and Pranhita; the Wardha, 
with its tributary the Penganga; and the Kistna, with its 
tributary the Tungabhadra. The climate may be considered 
in general good; and as there are no arid bare deserts, hot 
winds are little felt. 

More than half the revenue of the state is derived from the 
land, and the development of the country by irrigation and 
railways has caused considerable expansion in this revenue, 
though the rate of increase in the decade 1891-1901 was retarded 
by a succession of unfavourable seasons. The soil is generally 
fertile, though in some parts it consists of chilka, a red and gritty 
mould little fitted for purposes of agriculture. The principal 
crops are millets of various kinds, rice, wheat, oil-seeds, cotton. 



32 



HYDERABAD— HYDER ALI 



tobacco, sugar-cane, and fruits and garden produce in great 
variety. Silk, known as lussur, the produce of a wild species 
of worm, is utilized on a large scale. Lac, suitable for use as a 
resin or dye, gums and oils are found in great quantities. Hides, 
raw and tanned, are articles of some importance in commerce. 
The principal exports are cotton, oil-seeds, country-clothes 
and hides; the imports are salt, grain, timber, European piece- 
goods and hardware. The mineral wealth of the state consists 
of coal, copper, iron, diamonds and gold; but the development 
of these resources has not hitherto been very successful. The 
only coal mine now worked is the large one at Singareni, with an 
annual out-turn of nearly half a million tons. This coal has 
enabled the nizam's guaranteed state railway to be worked so 
cheaply that it now returns a handsome profit to the state. It 
also gives encouragement to much-needed schemes of railway 
extension, and to the erection of cotton presses and of spinning 
and weaving mills. The Hyderabad-Godavari railway (opened 
in 1901) traverses a rich cotton country, and cotton presses 
have been erected along the line. The currency of the state 
is based on the halt sikka, which contains approximately the 
same weight of silver as the British rupee, but its exchange 
value fell heavily after 1893, when free coinage ceased in the 
mint. In 1004, however, a new coin (the Mahbubia rupee) 
was minted; the supply was regulated, and the rate of exchange 
became about 115 = 100 British rupees. The state suffered from 
famine during 1900, the total number of persons in receipt of 
relief rising to nearly 500,000 in June of that year. The nizam 
met the demands for relief with great liberality. 

The nizam of Hyderabad is the principal Mahommedan ruler 
in India. The family was founded by Asaf Jah, a distinguished 
Turkoman soldier of the emperor Aurangzeb, who in 17 13 was 
appointed subahdar of the Deccan, with the title of nizam- 
ul-mulk (regulator of the state), but eventually threw off the 
control of the Delhi court. Azaf Jah's death in 1748 was followed 
by an internecine struggle for the throne among his descendants, 
in which the British and the French took part. At one time 
the French nominee, Salabat Jang, established himself with 
the help of Bussy. But finally, in 1761, when the British had 
secured their predominance throughout southern India, Nizam 
Ali took his place and ruled till 1803. It was he who confirmed 
the grant of the Northern Circars in 1766, and joined in the two 
wars against Tippoo Sultan in 1792 and 1799. The additions 
of territory which he acquired by these wars was afterwards 
(1800) ceded to the British, as payment for the subsidiary force 
which he had undertaken to maintain. By a later treaty in 
1853, the districts known as Berar were " assigned " to defray 
the cost of the Hyderabad contingent. In 1857 when the 
Mutiny broke out, the attitude of Hyderabad as the premier 
native state and the cynosure of the Mabommedans in India 
became a matter of extreme importance; but Afzul-ud-Dowla, 
the father of the present ruler, and his famous minister, Sir 
Salar Jang, remained loyal to the British. An attack on the 
residency was repulsed, and the Hyderabad contingent displayed 
their loyalty in the field against the rebels. In 1902 by a treaty 
made by Lord Curzon, Berar was leased in perpetuity to the 
British government, and the Hyderabad contingent was merged 
in the Indian army. The nizam Mir Mahbub Ali Khan Bahadur, 
Asaf Jah, a direct descendant of the famous nizam-ul-mulk, 
was born on the 18th of August 1866. On the death of his 
father in 1869 he succeeded to the throne as a minor, and was 
invested with full powers in 1884. He is notable as the originator 
of the Imperial Service Troops, which now form the contribution 
of the native chiefs to the defence of India. On the occasion 
of the Panjdeh incident in 1885 he made an offer of money and 
men, and subsequently on the occasion of Queen Victoria's 
Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three 
years for the purpose of frontier defence. It was finally decided 
that the native chiefs should maintain small but well-equipped 
bodies of infantry and cavalry for imperial defence. For many 
years past the Hyderabad finances were in a very unhealthy 
condition; the expenditure consistently outran the revenue, 
and the nobles, who held their tenure under an obsolete feudal 



system, vied with each other in ostentatious extravagance. 
But in 1902, on the revision of the Berar agreement, the nizam 
received 25 lakhs (£167,000) a year for the rent of Berar, thus 
substituting a fixed for a fluctuating source of income, and 
a British financial adviser was appointed for the purpose of 
reorganizing the resources of the state. 

See S. H. Bilgrami and C. Willmott, Historical and Descriptive 
Sketch of the Nizam's Dominions (Bombay, 1883-1884). 

HYDERABAD or Haidarabad, capital of the above state, 
is situated on the right bank of the river Musi, a tributary of 
the Kistna, with Golconda to the west, and the residency and 
its bazaars and the British cantonment of Secunderabad to the 
north-east. It is the fourth largest city in India; pop. (1901) 
448,466, including suburbs and cantonment. The city itself is 
in shape a parallelogram, with an area of more than 2 sq. m. 
It was founded in 1589 by Mahommed Kuli, fifth of the Kutb 
Shahi kings, of whose. period several important buildings remain 
as monuments. The principal of these is the Char Minar or 
Four Minarets (1591). The minarets rise from arches facing the 
cardinal points, and stand in the centre of the city, with four 
roads radiating from their base. The Ashur Khana (1594), a 
ceremonial building, the hospital, the Gosha Mahal palace and 
the Mecca mosque, a sombre building designed after a mosque 
at Mecca, surrounding a paved quadrangle 360 ft. square, were 
the other principal buildings of the Kutb Shahi period, though 
the mosque was only completed in the time of Aurangzeb. The 
city proper is surrounded by a stone wall with thirteen gates, 
completed in the time of the first nizam, who made Hyderabad 
his capital. The suburbs, of which the most important is 
Chadarghat, extend over an additional area of 9 sq. m. There 
are several fine palaces built by various nizams, and the British 
residency is an imposing building in a large park on the left 
bank of the Musi, N.E. of the city. The bazaars surrounding it, 
and under its jurisdiction, are extremely picturesque and are 
thronged with natives from all parts of India. Four bridges 
crossed the Musi, the most notable of which was the Furana 
Pul, of 23 arches, built in 1593. On the '27th and 28th of 
September 1908, however, the Musi, swollen by torrential rainfall 
(during which 15 in. fell in 36 hours), rose in flood to a height of 
12 ft. above the bridges and swept them away. The damage 
done was widespread ; several important buildings were involved, 
including the palace of Salar Jang and the Victoria zenana 
hospital, while the beautiful grounds of the residency were 
destroyed. A large and densely populated part of the city was 
wrecked, and thousands of lives were lost. The principal 
educational establishments are the Nizam college (first grade), 
engineering, law, medical, normal, industrial and Sanskrit 
schools, and a number of schools for Europeans and Eurasians. 
Hyderabad is an important centre of general trade, and there is a 
cotton mill in its vicinity. The city is supplied with water from 
two notable works, the Husain Sagar and the Mir Alam, both 
large lakes retained by great dams. Secunderabad, the British 
military cantonment, is situated s| m. N. of the residency; 
it includes Bolaram, the former headquarters of the Hyderabad 
contingent. 

HYDER ALI, or Haidar 'Ali (c. 1722-1782), Indian ruler 
and commander. This Mahommedan soldier-adventurer, who, 
followed by his son Tippoo, became the most formidable Asiatic 
rival the British ever encountered in India, was the great-grandson 
of & fakir or wandering ascetic of Islam, who had found his way 
from the Punjab to Gulburga in the Eeccan, and the second sen 
of a naik or chief constable at Budikota, near Kolar in Mysore. 
He was born in 1722, or according to other authorities 1717. 
An elder brother, who like himself was early turned out into 
the world to seek his own fortune, rose to command a brigade 
in the Mysore army, while Hyder, who never learned to read or 
write, passed the first years of his life aimlessly in sport and 
sensuality, sometimes, however, acting as the agent of his brother, 
and meanwhile acquiring a useful familiarity with the tactics 
of the French when at the height of their reputation under 
Dupleix. He is said to have induced his brother to employ a 
Parsee to purchase artillery and small arms from the Bombay 



HYDRA 



33 



government, and to enrol some thirty sailors of different European 
nations as gunners, and is thus credited with having been " the 
first Indian who formed a corps of sepoys armed with fire- 
locks and bayonets, and who had a train of artillery served by 
Europeans." At the siege of Devanhalli (1749) Hyder's services 
attracted the attention of Nanjiraj, the minister of the raja of 
Mysore, and he at once received an independent command; 
within the next twelve years his energy and ability had made 
him completely master of minister and raja alike, and in every- 
thing but in name he was ruler of the kingdom. In 1763 the 
conquest of Kanara gave him possession of the treasures of 
Bednor, which he resolved to make the most splendid capital 
in India, under his own name, thenceforth changed from Hyder 
Naik into Hyder Ali Khan Bahadur; and in 1765 he retrieved 
previous defeat at the hands of the Mahrattas by the destruction 
of the Nairs or military caste of the Malabar coast, and the 
conquest of Calicut. Hyder Ali now began to occupy the 
serious attention of the Madras government, which in 1766 
entered into an agreement with the nizam to furnish him with 
troops to be used against the common foe. But hardly had this 
alliance been formed when a secret arrangement was come to 
between the two Indian powers, the result of which was that 
Colonel Smith's small force was met with a united army of 
80,000 men and 100 guns. British dash and sepoy fidelity, 
however, prevailed, first in the battle of Chengam (September 3rd, 
1767), and again still more remarkably in that of Tiruvannamalai 
(Trinomalai). On the loss of his recently made fleet and forts 
on the western coast, Hyder Ali now offered overtures for peace; 
on the rejection of these, bringing all his resources and strategy 
into play, he forced Colonel Smith to raise the siege of Bangalore, 
and brought his army within 5 m. of Madras. The result was 
the treaty of April 1769, providing for the mutual restitution 
of all conquests, and for mutual aid and alliance in defensive 
war; it was followed by a commercial treaty in 1770 with the 
authorities of Bombay. Under these arrangements Hyder Ali, 
when defeated by the Mahrattas in 1772, claimed British assist- 
ance, but in vain; this breach of faith stung him to fury, and 
thenceforward he and his son did not cease to thirst for vengeance. 
His time came when in 1778 the British, on the declaration of 
war with France, resolved to drive the French out of India. 
The capture of Mahe on the coast of Malabar in 1779, followed 
by the annexation of lands belonging to a dependent of his own, 
gave him the needed pretext. Again master of all that the 
Mahrattas had taken from him, and with empire extended to the 
Kistna, he descended through the passes of the Ghats amid 
burning villages, reaching Conjeeveram, only 45 m. from Madras, 
unopposed. Not till the smoke was seen from St Thomas's 
Mount, where Sir Hector Munro commanded some 5200 troops, 
was any movement made; then, however, the British general 
sought to effect a junction with a smaller body under Colonel 
Baillie recalled from Guntur. The incapacity of these officers, 
notwithstanding the splendid courage of their men, resulted 
in the total destruction of Baillie's force of 2800 (September 
the 10th, 1780). Warren Hastings sent from Bengal Sir Eyre 
Coote, who, though repulsed at Chidambaram, defeated Hyder 
thrice successively in the battles of Porto Novo, Pollilur and 
Sholingarh, while Tippoo was forced to raise the siege of Wandi- 
vvash, and Vellore was provisioned. On the arrival of Lord 
Macartney as governor of Madras, the British fleet captured 
Negapatam, and forced Hyder Ali to confess that he could never 
ruin a power which had command of the sea. He had sent his 
son Tippoo to the west coast, to seek the assistance of the French 
fleet, when his death took place suddenly at Chittur in December 
1782. 

See L. B. Bowring, Haidar Ali and Tipu Sultan, " Rulers of India " 
series (1893). For the personal character and administration of 
Hyder Ali see the History of Hyder Naik, written by Mir Hussein Ali 
Khan Kirmani (translated from the Persian by Colonel Miles, and 
published by the Oriental Translation Fund), and the curious work 
written by M. Le Maitre de La Tour, commandant of his artillery 
{Histoire 'd'Hayder-AH Khan, Paris, 1783). For the whole life and 
times see Wilks, Historical Sketches of the South of India (1810-1817) ; 
\itchison's Treaties, vol. v. (2nd ed., 1876}; and Pearson, Memoirs 
of Schwartz (1834). 



HYDRA (or Sidra, Nidra, Idero, &c; anc. Hydrea), an 
island of Greece, lying about 4 m. off the S.E. coast of Argolis 
in the Peloponnesus, and forming along with the neighbouring 
island of Dokos (Dhoko) the Bay of Hydra. Pop. about 6200. 
The greatest length from south-west to north-east is about n m., 
and the area is about 21 sq. m.; but it is little better than a 
rocky and treeless ridge with hardly a patch or two of arable 
soil. Hence the epigram of Antonios Kriezes to the queen of 
Greece: " The island produces prickly pears in abundance, 
splendid sea captains and excellent prime ministers." The 
highest point, Mount Ere, so called (according to Mjaoules) 
from the Albanian word for wind, is 1958 ft. high. The next in 
importance is known as the Prophet Elias, from the large convent 
of that name on its summit. It was there that the patriot 
Theodorus Kolokotrones was imprisoned, and a large pine tree 
is still called after him. The fact that in former times the island 
was richly clad with woods is indicated by the name still employed 
by the Turks, Tchamliza, the place of pines; but it is only in 
some favoured spots that a few trees are now to be found. 
Tradition also has it that it was once a well-watered island 
(hence the designation Hydrea), but the inhabitants are now 
wholly dependent on the rain supply, and they have sometimes 
had to bring water from the mainland. This lack of fountains 
is probably to be ascribed in part to the effect of earthquakes, 
which are not infrequent; that of 1769 continued for six whole 
days. Hydra, the chief town, is built near the middle of the 
northern coast, on a very irregular site, consisting of three hills 
and the intervening ravines. From the sea its white and hand- 
some houses present a picturesque appearance, and its streets 
though narrow are clean and attractive. Besides the principal 
harbour, round which the town is built, there are three other 
ports on the north coast — Mandraki, Molo, Panagia, but none 
of them is sufficiently sheltered. Almost all the population 
of the island is collected in the chief town, which is the seat of a 
bishop, and has a local court, numerous churches and a high 
school. Cotton and silk weaving, tanning and shipbuilding 
are carried on, and there is a fairly active trade. 

Hydra was of no importance in ancient times. The only fact 
in its history is that the people of Hermione (a city on the 
neighbouring mainland now known by the common name of 
Kastri) surrendered it to Samian refugees, and that from these 
the people of Troezen received it in trust. It appears to be com- 
pletely ignored by the Byzantine chroniclers. In 1580 it was 
chosen as a refuge by a body of Albanians from Kokkinyas in 
Troezenia; and other emigrants followed in 1590, 1628, 1635, 
1640, &c. At the close of the 17th century the Hydriotes took 
part in the reviving commerce of the Peloponnesus; and in 
course of time they extended their range. About 17 16 they 
began to build sakturia (of from 10 to 15 tons burden), and to 
visit the islands of the Aegean; not long after they introduced 
the latinadika (40-50 tons), and sailed as far as Alexandria, 
Constantinople, Trieste and Venice; and by and by they 
ventured to France and even America. From the grain trade 
of south Russia more especially they derived great wealth. In 
1813 there were about 22,000 people in the island, and of these 
10,000 were seafarers. At the time of the outbreak of the war of 
Greek independence the total population was 28,190, of whom 
16,460 were natives and the rest foreigners. One of their chief 
families, the Konduriotti, was worth £2,000,000. Into the 
struggle the Hydriotes flung themselves with rare enthusiasm 
and devotion, and the final deliverance of Greece was mainly 
due to the service rendered by their fleets. 

See Pouqueville, Voy. de la Grece, vol. vi. ; Antonios Miaoules, 
"twofimi^a irtpl rijs vf)<rov "TSpas (Munich, 1834); Id. XvvoirTLKr) laropla 
rccv vaviiax&v 5ta roiv tt\o'uav ToivrpUov vt)<twv, "TSpas, Xleraiov Kal ^apup 
(Nauplia, 1833); Id. 'Ioropia rffi vrjcrov "TSpas (Athens, 1874); G. D. 
Kriezes, 'Ioropia rrjs vrjcrov "TSpas (Patras, i860). 

HYDRA (watersnake), in Greek legend, the offspring of Typhon 

and Echidna, a gigantic monster with nine heads (the number 

is variously given), the centre one being immortal. Its haunt 

was a hill beneath a plane tree near the river Amymone, in the 

I marshes of Lerna by Argos. The destruction of this Lernaean 



34 



HYDRA—HYDRATE 



hydra was one of the twelve " labours " of Heracles, which he 
accomplished with the assistance of Iolaus. Finding that as 
soon as one head was cut off two grew up in its place, they burnt 
out the roots with firebrands, and at last severed the immortal 
head from the body, and buried it under a mighty block of rock. 
The arrows dipped by Heracles in the poisonous blood or gall 
of the monster ever afterwards inflicted fatal wounds. The 
generally accepted interpretation of the legend is that " the 
hydra denotes the damp, swampy ground of Lerna with its 
numerous springs (necpaXai, heads) ; its poison the miasmic 
vapours rising from the stagnant water; its death at the hands 
of Heracles the introduction of the culture and consequent 
purification of the soil " (Preller). A euhemeristic explanation 
is given by Palaephatus (39). An ancient king named Lernus 
occupied a small citadel named Hydra, which was defended 
by 50 bowmen. Heracles besieged the citadel and hurled 
firebrands at the garrison. As often as one of the defenders 
fell, two others at once stepped into his place. The citadel 
was finally taken with the assistance of the army of Iolaus and 
the garrison slain. 

See Hesiod, Theog., 313; Euripides, Hercules furens, 419; 
Pausanias ii. 37; Apollodorus ii. 5, 2; Diod. Sic. iv. n; Roscher's 
Lexikon der Mythologie. In the article Greek Art, fig. 20 represents 
the slaying of the Lernaean hydra by Heracles. 

HYDRA, in astronomy, a constellation of the southern 
hemisphere, mentioned by Eudoxus (4th century B.C.) and 
Aratus (3rd century B.C.), and catalogued by Ptolemy (27 stars), 
Tycho Brahe (19) and Hevelius (31). Interesting objects are: 
the nebula H. I V. 27 Hydrae, a planetary nebula, gaseous and 
whose light is about equal to an 8th magnitude star; e Hydrae, 
a beautiful triple star, composed of two yellow stars of the 4th 
and 6th magnitudes, and a blue star of the 7th magnitude; 
R. Hydrae, a long period (425 days) variable, the range in 
magnitude being from 4 to 9-7; and U. Hydrae, an irregularly 
variable, the range in magnitude being 4-5 to 6. 

HYDRACRYLIC ACID (ethylene lactic acid), CH 2 OH-CH 2 - 
C0 2 H. an organic oxyacid prepared by acting with silver oxide and 
water on /3-iodopropionic acid, or from ethylene by the addition 
of hypochlorous acid, the addition product being then treated 
with potassium cyanide and hydrolysed by an acid. It may 
also be prepared by oxidizing the trimethylene glycol obtained 
by the action of hydrobromic acid on allylbromide. It is a 
syrupy liquid, which on distillation is resolved into water and 
the unsaturated acrylic acid, CII2: CH-C0 2 H. Chromic and 
nitric acids oxidize it to oxalic acid and carbon dioxide. 
Hydracrylic aldehyde, CH 2 OH-CH 2 -CHO, was obtained in 1904 
by J. U. Nef (Ann. 335, p. 219) as a colourless oil by heating 
acrolein with water. Dilute alkalis convert it into crotonalde- 
hyde, CH r CH : CH-CHO. 

HYDRANGEA, a popular flower, the plant to which the name 
is most commonly applied being Hydrangea Hortensia, a low 
deciduous shrub, producing rather large oval strongly-veined 
leaves in opposite pairs along the stem. It is terminated by 
a massive globular corymbose head of flowers, which remain a 
long period in an ornamental condition. The normal colour 
of the flowers, the majority of which have neither stamens nor 
pistil, is pink; but by the influence of sundry agents in the soil, 
such as alum or iron, they become changed to blue. There are 
numerous varieties, one of the most noteworthy being " Thomas 
Hogg " with pure white flowers. The part of the inflorescence 
which appears to be the flower is an exaggerated expansion of 
the sepals, the other parts being generally abortive. The perfect 
flowers are small, rarely produced in the species above referred 
to, but well illustrated by others, in which they occupy the inner 
parts of the corymb, the larger showy neuter flowers being 
produced at the circumference. 

There are upwards of thirty species, found chiefly in Japan, 
ki the mountains of India, and in North America, and many of 
them are familiar in gardens. H. Hortensia (a species long 
known in cultivation in China and Japan) is the most useful 
for decoration, as the head of flowers lasts long in a fresh state, 
and by the aid of forcing can be had for a considerable period 



for the ornamentation of the greenhouse and conservatory. 
Their natural flowering season is towards the end of the summer, 
but they may be had earlier by means of forcing. H . japonica 
is another fine conservatory plant, with foliage and habit much 
resembling the last named, but this has flat corymbs of flowers, 
the central ones small and perfect, and the outer ones only 
enlarged and neutei. This also produces pink or blue flowers 
under the influence of different soils. 

The Japanese species of hydrangea are sufficiently hardy 
to grow in any tolerably favourable situation, but except in 
the most sheltered localities they seldom blossom to any degree 
of perfection in the open air, the head of blossom depending 
on the uninjured development of a well-ripened terminal bud, 
and this growth being frequently affected by late spring frosts. 
They are much more useful for pot-culture indoors, and should 
be reared from cuttings of shoots having the terminal bud plump 
and prominent, put in during summer, these developing a single 
head of flowers the succeeding summer. Somewhat larger 
plants may be had by nipping out the terminal bud and inducing 
three or four shoots to start in its place, and these, being steadily 
developed and well ripened, should each yield its inflorescence 
in the following summer, that is, when two years old. Large 
plants grown in tubs and vases are fine subjects for large con- 
servatories, and useful for decorating terrace walks and similar 
places during summer, being - housed in winter, and started 
under glass in spring. 

Hydrangea paniculata var. grandiflora is a very handsome 
plant; the branched inflorescence under favourable circum- 
stances is a yard or more in length, and consists of large spreading 
masses of crowded white neuter flowers which completely conceal 
the few inconspicuous fertile ones. The plant attains a height 
of 8 to 10 ft. and when in flower late in summer and in autumn 
is a very attractive object in the shrubbery. 

The Indian and American species, especially the latter, are 
quite hardy, and some of them are extremely effective. 

HYDRASTINE, C 21 H 2 iN0 6 , an alkaloid found with berberine 
in the root of golden seal, Hydrastis canadensis, a plant indigenous 
to North America. It was discovered by Durand in 1851, and 
its chemistry formed the subject of numerous communications 
by E. Schmidt and M. Freund (see Ann., 1892, 271, p. 311) 
who, aided by P. Fritsch {Ann., 1895, 286, p. 1), established 
its constitution. It is related to narcotine, which is methoxy 
hydrastine. The root of golden seal is used in medicine under 
the name hydrastis rhizome, as a stomachic and nervine 
stimulant. 

HYDRATE, in chemistry, a compound containing the elements 
of water in combination; more specifically, a compound contain- 
ing the monovalent hydroxyl or OH group. The first and more 
general definition includes substances containing water of 
crystallization; such salts are said to be hydrated, and when 
deprived of their water to be dehydrated or anhydrous. Com- 
pounds embraced by the second definition are more usually 
termed hydroxides, since -at one time they were regarded as com- 
binations of an oxide with water, for example, calcium oxide or 
lime when slaked with water yielded calcium hydroxide, written 
formerly as CaO-H 2 0. The general formulae of hydroxides 
are: M'OH, M ii (OH) 2 ,M iii (OH) 3 ,M iv (OH) 4 ,&c, corresponding 
to the oxides M 2 i O, M u O, M 2 iU 3 , M iv 2 , &c, the Roman index 
denoting the valency of the element. There is an important 
difference between non-metallic and metallic hydroxides; 
the former are invariably acids (oxyacids), the latter are more 
usually basic, although acidic metallic oxides yield acidic 
hydroxides. Elements exhibiting strong basigenic or oxygenic 
characters yield the most, stable hydroxides; in other words, 
stable hydroxides are associated with elements belonging to the 
extreme groups of the periodic system, and unstable hydroxides 
with the central members. The most stable basic hydroxides 
are those of the alkali metals, viz. lithium, sodium, potassium, 
rubidium and caesium, and of the alkaline earth metals, viz. 
calcium, barium and strontium; the most stable acidic hydroxides 
are those of the elements placed in groups VB, VIB and VIIB 
of the periodic table. 



HYDRAULICS 



35 



HYDRAULICS (Gr. SScop, water, and auXos, a pipe), the branch 
of engineering science which deals with the practical applications 
of the laws of hydromechanics. 

I. THE DATA OF HYDRAULICS ' 

§ i. Properties of Fluids. — The fluids to which the laws of 
practical hydraulics relate are substances the parts of which 
possess very great mobility, or which offer a very small resistance 
to distortion independently of inertia. Under the general 
head'ig Hydromechanics a fluid is denned to be a substance 
which yields continually to the slightest tangential stress, and 
hence in a fluid at rest there can be no tangential stress. But, 
further, in fluids such as water, air, steam, &c, to which the 
present division of the article relates, the tangential stresses 
that are called into action between contiguous portions during 
distortion or change of figure are always small compared with 
the weight, inertia, pressure, &c, which produce the visible 
motions it is the object of hydraulics to estimate. On the other 
hand, while a fluid passes easily from one form to another, it 
opposes considerable resistance to change of volume. 

It is easily deduced from the absence or smallness of the 
tangential stress that contiguous portions of fluid act on each 
other with a pressure which is exactly or very nearly normal 
to the interface which separates them. The stress must be a 
pressure, not a tension, or the parts would separate. Further, 
at any point in a fluid the pressure in all directions must be the 
same; or, in other words, the pressure on any small element 
of surface is independent of the orientation of the surface. 

§ 2. Fluids are divided into liquids, or incompressible fluids, 
and gases, or compressible fluids. Very great changes of pressure 
change the volume of liquids only by a small amount, and if 
the pressure on them is reduced to zero they do not sensibly 
dilate. In gases or compressible fluids the volume alters sensibly 
for small changes of pressure, and if the pressure is indefinitely 
diminished they dilate without limit. 

In ordinary hydraulics, liquids are treated as absolutely 
incompressible. In dealing with gases the changes of volume 
which accompany changes of pressure must be taken into 
account. 

§ 3. Viscous fluids are those in which change of form under a 
continued stress proceeds gradually and increases indefinitely. 
A very viscous fluid opposes great resistance to change of form 
in a short time, and yet may be deformed considerably by a 
small stress acting for a long period. A block of pitch is more 
easily splintered than indented by a hammer, but under the 
action of the mere weight of its parts acting for a long enough 
time it flattens out and flows like a liquid. 

All actual fluids are viscous. They oppose a resistance 
to the relative motion of their parts. This resistance diminishes 
with the velocity of the relative motion, and becomes zero 
in a fluid the parts of which are relatively at rest. When the 
relative motion of different parts of a fluid is small, the viscosity 
may be neglected without introducing important errors. On 
the other hand, where there is considerable relative motion, 

the viscosity may be ex- 
"tL» pected to have an influence 
too great to be neglected. 

Measurement of Viscosity. 
Coefficient of Viscosity. — 
Suppose the plane ab. fig. z 
of area a, to move with the 
velocity V relative.lv to the 
surface cd and parallel to it. 




Fig. 1. 



Let the space between be filled with liquid. The layers of liquid 
in contact with ab and cd adhere to them. The intermediate layers 
all offering an equal resistance to shearing or distortion, the rect- 
angle of fluid abed will take the form of the parallelogram a'b'cd. 
Further, the resistance to the motion of ab may be expressed in 
the form 

R = /c M V, (1) 

where k is a coefficient the nature of which remains to be deter- 
mined. 



' Except where other units are given, the units throughout this 
article are feet, pounds, pounds per sq. ft., feet per second. 



If we suppose the liquid between ab and cd divided into layers as 
shown in fig. 2, it will be clear that the stress R acts, at each dividing 
face, forwards in the direction of motion if we consider the upper 
layer, backwards if we consider the lower layer. Now suppose the 
original thickness of the layer T increased to »T; if the bounding 
plane in its new position has the velocity «V, the shearing at each 
dividing face will be exactly the same as before, and the resistance 
must therefore be the same. Hence, 

R = k'w(mV). (2) 

But equations (1) and (2) may both be expressed in one equation if 
k and k' are replaced by a constant varying inversely as the thickness 
of the layer. Putting k =m/T. k' —n/nt, 
R= M oV7T; 
or, for an indefinitely thin layer, 

R =na>dVldt, (3) 

an expression first proposed by L. M. H. Navier. The coefficient m is 
termed the coefficient of viscosity. 

According to J. Clerk Maxwell, the value of m for air at 0° Fahr. in 
pounds, when the velocities are expressed in feet per second, is 

ix = o-ooo 000 025 6(46i°-f-0); 
that is, the coefficient of viscosity is proportional to the absolute 
temperature and independent of the pressure. 

The value of « for water at 77° Fahr. is, according to H. von 
Helmholtz and G. Piotrowski, 

M = o-ooo 018 8, 
the units being the same as before. For water p decreases rapidly 
with increase of temperature. 

§ 4. When a fluid flows in a very regular manner, as for instance 
when it flows in a capillary tube, the velocities vary gradually 
at any moment from 

one point of the fluid i, 2 V- - - ^ 

to a neighbouring „ r !_.' [TJZ'.'S-'SZZZZZZZZZZ 

point. The layer ad- 
jacent to the sides of 
the tube adheres to it 
and is at rest. The 
layers more interior 
than this slide on each 
other. But the resist- 
ance developed by 
these regular move- 
ments is very small. If 
in large pipes and open 
channels.there were a 
similar regularity of movement, the neighbouring filaments 
would acquire, especially near the sides, very great relative 
velocities. V. J. Boussinesq has shown that the central filament 
in a semicircular canal of 1 metre radius, and inclined at a slope 
of only o-oooi, would have a velocity of 187 metres per second, 2 
the layer next the boundary remaining at rest. But before 
such a difference of velocity can arise, the motion of the fluid 
becomes much more complicated. Volumes of fluid are detached 
continually from the boundaries, and, revolving, form eddies 
traversing the fluid in all directions, and sliding with finite 
relative velocities against those surrounding them. These 
slidings develop resistances incomparably greater than the 
viscous resistance due to movements varying continuously from 
point to point. The movements which produce the phenomena 
commonly ascribed to fluid friction must be regarded as rapidly 
or even suddenly varying from one point to another. The 
internal resistances to the motion of the fluid do not depend 
merely on the general velocities of translation at different points 
of the fluid (or what Boussinesq terms the mean local velocities), 
but rather on the intensity at each point of the eddying agitation. 
The problems of hydraulics are therefore much more complicated 
than problems in which a regular motion of the fluid is assumed, 
hindered by the viscosity of the fluid. 

Relation of Pressure, Density, asd Temperature 
of Liquids 

§ 5. Units of Volume. — In practical calculations the cubic foot 
and gallon are largely used, and in metric countries the litre and 
cubic metre ( = 1000 litres). The imperial gallon is now exclusively 
used in England, but the United States have retained the old English 
wine gallon. 

2 Journal de M. Liouville, t. xiii. (1868); Memoires de I' Academic, 
des Sciences de I'Institut de France, t. xxiii., xxiv. (1877). 




36 



HYDRAULICS 



[KINEMATICS OF FLUIDS 



I cub. ft. = 6-236 imp. gallons 

1 imp. gallon = 0-1605 cub. ft. 

1 U.S. gallon = 0-1337 cub. ft. 

I litre = 0-2201 imp. gallon 



= 7-481 U.S. gallons. 
= 1 -200 U.S. gallons. 
= 0-8333 imp. gallon. 
= 0-2641 U.S. gallon. 

Density of Water. — Water at 53° F. and ordinary pressure contains 
62-4 ft per cub. ft., or 10 lb per imperial gallon at 62° F. The litre 
contains one kilogram of water at 4 C. or 1000 kilograms per cubic 
metre. River and spring water is not sensibly denser than pure 
water. But average sea water weighs 64 lb per cub. ft. at 53° F. 
The weight of water per cubic unit will be denoted by G. Ice free 
from air weighs 57-28 ft per cub. ft. (Leduc). 

§ 6. Compressibility of Liquids. — The most accurate experiments 
show that liquids are sensibly compressed by very great pressures, 
and that up to a pressure of 65 atmospheres, or about 1000 lb per 
sq. in., the compression is proportional to the pressure. The chief 
results of experiment are given in the following table. Let Vi be 
the volume of a liquid in cubic feet under a pressure pi lb per sq. ft., 
and V2 its volume under a pressure pi. Then the cubical compres- 
sion is (V2 — Vi)/Vi, and the ratio of the increase of pressure 
pi— pi to the cubical compression is sensibly constant. That is, 
k — (,p2~ pi)\'il(Vz — Vi) is constant. This constant is termed the 
elasticity of volume. With the notation of the differential calculus, 



'-»/(-$)-- 



-V 



dp 
dV 





Elasticity of Volume of Liquids. 






Canton. 


Oersted. 


Colladon 
and Sturm. 


Regnault. 


Water . . 
Sea water 
Mercury 
Oil . . . 
Alcohol 


45,990,000 
52,900,000 
705,300,000 
44,090,000 
32,060,000 


45,900,000 


42,660,000 

626,100,000 

23,100,000 


44,090,000 
604,500,000 



According to the experiments of Grassi, the compressibility of 
water diminishes as the temperature increases, while that of ether, 
alcohol and chloroform is increased. 

§ 7. Change of Volume and Density of Water with Change of Tem- 
perature. — Although the change of volume of water with change of 
temperature is so small that it may generally be neglected in ordinary 
hydraulic calculations, yet it should be noted that there is a change 
of volume which should be allowed for in very exact calculations. 
The values of p in the following short table, which gives data enough 
for hydraulic purposes, are taken from Professor Everett's System 
of Units. 

Density of Water at Different Temperatures. 



Temperature. 


P 


G 1 


Temperature. 


p 


G 




ensity of 
Water. 


Weight of 




Density of 
Water. 


Weight of 


Cent. 


Fahr. 


1 cub. ft. 

in TK ' 


Cent. 


Fahr. 


1 cub. ft. 
in It). 





320 


999884 


62-417 


20 


68-o 


•998272 


62316 


I 


33*8 


999941 


62-420 


22 


71-6 


•997839 


62-28Q 


2 


35-6 


999982 


62-423 


24 


75-2 


•997380 


62-26I 


3 


37-4 1 


OOOO04 


62-424 


26 


78-8 


•996879 


62229 


4 


39-2 1 


OOOO13 


62-425 


28 


82-4 


•996344 


62-196 


5 


41-0 1 


OOOOO3 


62-424 


30 


86 


•995778 


62-I6I 


6 


42-8 


999983 


62-423 


35 


95 


•99469 


62-093 


7 


44-6 


999946 


62-421 


40 


104 


■99236 


61-947 


8 


46-4 


999899 


62-418 


45 


"3 


•99038 


61-823 


9 


48-2 


999837 


62-414 


50 


122 


•9882I 


61-688 


10 


50-0 


999760 


62-409 


55 


131 


•98583 


61-540 


11 


5i-8 


999668 


62-403 


60 


140 


•98339 


61-387 


12 


53-6 


999562 


62-397 


65 


149 


•98075 


61-222 


'3 


55-4 


999443 


62-389 


70 


158 


•97795 


61-048 


14 


57-2 


999312 


62-381 


75 


167 


•97499 


60-863 


15 


59-0 


999173 


62-373 


80 


176 


•97195 


60-674 


16 


6o-8 


999015 


62-363 


85 


185 


•96880 


60-477 


17 


62-6 


998854 


62-353 


90 


194 


•96557 


60-275 


18 


64-4 


998667 


62-341 


100 


212 


•95866 


59-844 


19 


66-2 


•998473 


62-329 









The weight per cubic foot has been calculated from the values of 
p, on the assumption that 1 cub. ft. of water at 39-2° Fahr. is 62-425 ft. 
For ordinary calculations in hydraulics, the density of water (which 
will in future be designated by the symbol G) will be taken at 62-4 ft 
per cub. ft., which is its density at 53° Fahr. It may be noted also 
that ice at 32° Fahr. contains 57-3 ft per cub. ft. The values of p 
are the densities in grammes per cubic centimetre. 

§ 8. Pressure Column. Free Surface Level. — Suppose a small 
vertical pipe introduced into a liquid at any point P (fig. 3). Then 
the liquid will rise in the pipe to a level 00, such that the pressure 
due to the column in the pipe exactly balances the pressure on its 
mouth. If the fluid is in motion the mouth of the pipe must be 
supposed accurately parallel to the direction of motion, or the 
impact of the liquid at the mouth of the pipe will have an influence 
on the height of the column. If this condition is complied with, 



the height h of the column is a measure of the pressure at the point 
P. Let o> be the area of section of the pipe, h the height of the 
pressure column, p the intensity of pressure at P; then 

pw=Ghoi%, 

p/G = h; 
that is, h is the height due to the pressure at p. The level 00 will 
be termed the free surface level corresponding to the pressure 
at P. 

Relation of Pressure, Temperature, and Density of Gases 

§ 9. Relation of Pressure, Volume, Temperature and Density in 
Compressible Fluids. — Certain problems on the flow of air and 
steam are so similar to 
those relating to the flow 
of water that they are 
conveniently treated 
together. It is neces- 
sary, therefore, to state as 
briefly as possible the 
properties ol compres- 
sible fluids so far as know- 
ledge of them is requisite 
in the solution of these 
problems. Air may be 
taken as a type of these 
fluids, and the numerical 
data here given will relate 
to air. 

Relation of Pressure 




Fig. 3. 



and Volume at Constant Temperature. — At constant temperature 
the product of the pressure p and volume V of a given quantity of 
air is a constant (Boyle's law). 

Let po be mean atmospheric pressure (2116-8 ft per sq. ft.), Vo 
the volume of 1 ft of air at 32° Fahr. under the pressure po. Then 
poVo = 26214. (1) 

If Go is the weight per cubic foot of air in the same conditions, 

Go = i/Vo = 2ii6-8/262i4 = -o8o75. (2) 

For any other pressure p, at which the volume of 1 ft is V and the 
weight per cubic foot is G, the temperature being 32° Fahr., 

pV= p!G =26214; or G=£/262i4. (3) 

Change of Pressure or Volume by Change of Temperature. — Let pn, 
Vo, Go, as before be the pressure, the volume of a pound in cubic feet, 
and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G 
be the same quantities at a temperature / (measured strictly by the 
air thermometer, the degrees of which differ a little from those of 
a mercurial thermometer). Then, by experiment, 

£V = £oVo(46o-6+/)/(46o-6+32) =A,V t/t , (4) 

where t, t are the temperatures / and 32° reckoned from the absolute 
zero, which is —460-6 Fahr. ; 

pjG = £ot/Got ; (4a) 

G=pT Go/poT. (5) 

If £0 = 2116-8, Go = -08075, to = 460-6+32 =492-6, then 

p/G = 53-27-. (5a) 

Or quite generally p/G = Rt for all gases, if R is a constant varying 
inversely as the density of the gas at 32° F. For steam R = 85-5- 

II. KINEMATICS OF FLUIDS 

§ 10. Moving fluids as commonly observed are conveniently 
classified thus: 

(1) Streams are moving masses of indefinite length, completely 
or incompletely bounded laterally by solid boundaries. When 
the solid boundaries are complete, the flow is said to take place 
in a pipe. When the solid boundary is incomplete and leaves 
the upper surface of the fluid free, it is termed a stream bed or 
channel or canal. 

(2) A stream bounded laterally by differently moving fluid 
of the same kind is termed a current. 

(3) A jet is a stream bounded by fluid of a different kind. 

(4) An eddy, vortex or whirlpool is a mass of fluid the particles 
of which are moving circularly or spirally. 

(5) In a stream we may often regard the particles as flowing 
along definite paths in space. A chain of particles following 
each other along such a constant path may be termed a fluid 
filament or elementary stream. 

§ 11. Steady and Unsteady, Uniform and Varying, Motion. — There 
are two quite distinct ways of treating hydrodynamical questions. 
We may either fix attention on a given mass of fluid and consider 
its changes of position and energy under the action of the stresses 
to which it is subjected, or we may have regard to a given fixed 
portion of space, and consider the volume and energy of the fluid 
entering and leaving that space. 



KINEMATICS OF FLUIDS] 



HYDRAULICS 



37 



If, in following a given path ab (fig. 4), a mass of water a has a 

constant velocity, the motion is said to be uniform. The kinetic 

energy of the mass a remains unchanged. If the velocity varies 

from point to point of the path, the motion is called varying motion. 

If at a given point a in space, the particles of water always arrive 

with the same velocity and in the same direction, during any given 

time, then the motion is termed steady motion. On the contrary, 

if at the point a the velocity or direction varies from moment to 

moment the motion is termed 
a. 

— a 



Fig. 4. 



unsteady. A river which ex- 
cavates its own bed is in 
unsteady motion so long as 
the slope and form of the bed 
is changing. It, however, 



tends always towards a condition in which the bed ceases to change, 
and it is then said to have reached a condition of permanent regime. 
No river probably is in absolutely permanent regime, except perhaps 
in rocky channels. In other cases the bed is scoured more or less 
during the rise of a flood, and silted again during the subsidence of 
the flood. But while many streams of a torrential character change 
the condition of their bed often and to a large extent, in others the 
changes are comparatively small and not easily observed. 

As a stream approaches a condition of steady motion, its regime 
becomes permanent. Hence steady motion and permanent regime 
are sometimes used as meaning the same thing. The one, however, 
is a definite term applicable to the motion of the water, the other a 
less definite term applicable in strictness only to the condition of 
the stream bed. 

§ 12. Theoretical Notions on the Motion of Water. — The actual 
motion of the particles of water is in most cases very complex. To 
simplify hydrodynamic problems, simpler modes of motion are 
assumed, and the results of theory so obtained are compared ex- 
perimentally with the actual motions. 

Motion in Plane Layers. — The simplest kind of motion in a stream 
is one in which the particles initially situated in any plane cross 

section of the stream con- 
tinue to be found in plane 
cross sections during the 
subsequent motion. Thus, 
if the particles in a thin 
plane layer ab (fig. 5) are 
found again in a thin plane 
layer a'V after any interval 
of time, the motion is said 
to be motion in plane layers. In such motion the internal work 
in deforming the layer may usually be disregarded, and the resist- 
ance to the motion is confined to the circumference. 
. Laminar Motion. — In the case of streams having solid boundaries, 
it is observed that the central parts move faster than the lateral 
parts. To take account of these differences of velocity, the stream 
may be conceived to be divided into thin laminae, having cross 
sections somewhat similar to the solid boundary of the stream, and 
sliding on each other. The different laminae can then be treated 
as having differing velocities according to any law either observed 
or deduced from their mutual friction. A much closer approxima- 
tion to the real motion of ordinary streams is thus obtained. 

Stream Line Motion. — In the preceding hypothesis, all the particles 
in each lamina have the same velocity at any given cross section of 
the stream. If this assumption is abandoned, the cross section of 
the stream must be supposed divided into indefinitely small areas, 
each representing the section of a fluid filament. Then these fila- 
ments may have any law of variation of velocity assigned to them. 
If the motion is steady motion these fluid filaments (or as they are 
then termed stream lines) will have fixed positions in space. 

Periodic Unsteady Motion. — In ordinary streams with rough 
boundaries, it is observed that at any given point the velocity varies 
from moment to moment in magnitude and direction, but that the 
average velocity for a sensible period (say for 5 or 10 minutes) 
varies very little either in magnitude or velocity. It has hence 




Fig. 5. 



be the velocity of the fluid. Then the volume flowing through the 
surface A in unit time is 

Q=coV. _ (1) 

Thus, if the motion is rectilinear, all the particles at any instant in 
the surface A will be found after one second in a similar surface A', 
at a distance V, and as each particle is followed by a continuous 
thread of other particles, the volume of flow is the right prism AA' 
having a base w and length V. 

If the direction of motion makes an angle 8 with the normal to 
the surface, the volume of flow is represented by an oblique prism 
AA' (fig. 7), and in that case 

Q = wV cos 9. 

If the velocity varies at different points of the surface, let the sur- 
face be divided into very small portions, for each of which the 



W»- 




V 



Fig. 6. 



been conceived that the variations of direction and magnitude of 
the velocity are periodic, and that, if for each point of the stream the 
mean velocity and direction of motion were substituted for the 
actual more or less varying motions, the motion of the stream 
might be treated as steady stream line or steady laminar 
motion. 

§ 13. Volume of Flow. — Let A (fig. 6) be any ideal plane surface, 
of area u>, in a stream, normal to the direction of motion, and let V 





W» 



Fig. 7. 

velocity may be regarded as constant. If da is the area and v, or 
v cos 0, the normal velocity for this element of the surface, the 
volume of flow is 

Q =fvdo>, or fv cos 9 da, 
as the case may be. 

§ 14. Principle of Continuity. — If we consider any completely 
bounded fixed space in a moving liquid initially and finally filled 
continuously with liquid, the inflow must be equal to the outflow. 
Expressing the inflow with a positive and the outflow with a negative 
sign, and estimating the volume of flow Q for all the boundaries, 

S Q=.°- 

In general the space will remain filled with fluid if the pressure 
at every point remains positive. There will be a break of continuity, 
if at any point the pressure becomes negative, indicating that the 
stress at that point is tensile. In the case of ordinary water this 
statement requires modification. Water contains a variable amount 
of air in solution, often about one-twentieth of its volume. This air 
is disengaged and breaks the continuity of the liquid, if the pressure 
falls below a point corresponding to its tension. It is for this reason 
that pumps will not draw water to the full height due to atmospheric 
pressure. 

Application of the Principle of Continuity to the case of a Stream. — 
If Ai, A2 are the areas of two normal cross sections of a stream, 
and Vi, V 2 are the velocities of the stream at those sections, then 
from the principle of continuity, 

ViA^ViA; 

V 1 /V 2 =A 2 /A 1 (2) 

that is, the normal velocities are inversely as the areas of the cross 
sections. This is true of the mean velocities, if at each section the 
velocity of the stream varies. In a river of varying slope the velocity 
varies with the slope. It is easy therefore to see that in parts of 
large cross section the slope is smaller than in parts of small cross 
section. 

If we conceive a space in a liquid bounded by normal sections at 
Ai, A 2 and between Ai, A 2 by stream lines (fig. 8), then, as there 
is no flow across the stream lines, 

V 1 /V 2 = A 2 /A I , 
as in a stream with rigid boundaries. 

In the case of compressible fluids the variation of volume due to 
the difference of pressure at the two sections must be taken into 




Fig. 8. 

account. If the motion is steady the weight of fluid between two 
cross sections of a stream must remain constant. Hence the weight 
flowing in must be the same as the weight flowing out. Let pi, pz 
be the pressures, v x , v 2 the velocities, Gi, G 2 the weight per cubic foot 
of fluid, at cross sections of a stream of areas Ai, A 2 . The volumes 
of inflow and outflow are 

Ai»i and A 2 t> 2 , 
and, if the weights of these are the same, 

GiAi!>i = G 2 A 2 z> 2 ; 
and hence, from (50) § 9, if the temperature is constant, 

piAiVi=p 2 A 2 v 2 . (3) 



38 



HYDRAULICS 



[DISCHARGE OF LIQUIDS 



§ IS. Stream Lines. — The characteristic of a perfect fluid, that is, 
a fluid free from viscosity, is that the pressure between any two parts ' 
into which it is divided by a plane must be normal to the plane. 
One consequence of this is that the particles can have no rotation 
impressed upon them, and the motion of such a fluid is irrotational. 
A stream line is the line, straight or curved, traced by a particle in 
a current of fluid in irrotational movement. In a steady current 





Fig. 9. 

each stream line preserves its figure and position unchanged, and 
marks the track of a stream of particles forming a fluid filament 
or elementary stream. A current in steady irrotational movement 
may be conceived to be divided by insensibly thin partitions follow- 
ing the course of the stream lines into a number of elementary 
streams. If the positions of these partitions are so adjusted that 
the volumes of flow in all the elementary streams are equal, they 
represent to the mind the velocity as well as the direction of motion 
of the particles in different parts of the current, for the velocities 





"r 




Fig. 11. 



Fig. 12. 



are inversely proportional to the cross sections of the elementary 
streams. No actual fluid is devoid of viscosity, and the effect of 
viscosity is to render the motion of a fluid sinuous, or rotational or 
eddying under most ordinary conditions. At very low velocities 
in a tube of moderate size the motion of water may be nearly pure 
stream line motion. But at some velocity, smaller as the diameter 
of the tube is greater, the motion suddenly becomes tumultuous. 
The laws of simple stream line motion have hitherto been investi- 
gated theoretically, and from mathematical difficulties have only 
been determined for certain simple cases. Professor H. S. Hele 
Shaw has found means of exhibiting stream 
line motion in a number of very interesting 
cases experimentally. Generally in these ex- 
periments a thin sheet of fluid is caused to flow 
between two parallel plates of glass. In the 
earlier experiments streams of very small air 
bubbles introduced into the water current 
rendered visible the motions of the water. By 
the use of a lantern the image of a portion of 
the current can be shown on a screen or photo- 
graphed. In later experiments streams of 
coloured liquid at regular distances were intro- 
duced into the sheet and these much more 
clearly marked out the forms of the stream 
lines. With a fluid sheet 0-02 in. thick, the 
stream lines were found to be stable at almost 
any required velocity. For certain simple 
cases Professor Hele Shaw has shown that the 
experimental stream lines of a viscous fluid are 
so far as can be measured identical with the calculated stream lines of 
a perfect fluid. Sir G. G. Stokes pointed out that in this case, either 
from the thinness of the stream between its glass walls, or the 
slowness of the motion, or the high viscosity of the liquid, or from 
a combination of all these, the flow is regular, and the effects of 
inertia disappear, the viscosity dominating everything. Glycerine 
gives the stream lines very satisfactorily. 

Fig. 9 shows the stream lines of a sheet of fluid passing a fairly 




Fig. 13. 



shipshape body such as a screwshaft strut. The arrow shows the 
direction of motion of the fluid. Fig. 10 shows the stream lines for 
a very thin glycerine sheet passing a non-shipshape body, the 
stream lines being practically perfect. Fig. II shows one of the 
earlier air-bubble experiments with a thicker sheet of water. In 
this case the stream lines break up behind the obstruction, forming 
an eddying wake. Fig. 12 shows the stream lines of a fluid passing 
a sudden contraction or sudden enlargement of a pipe. Lastly, 
fig. 13 shows the stream lines of a current passing an oblique plane. 
H. S. Hele Shaw, " Experiments on the Nature of the Surface Re- 
sistance in Pipes and on Ships," Trans. Inst. Naval Arch. (1897). 
" Investigation of Stream Line Motion under certain Experimental 
Conditions," Trans. Inst. Naval Arch. (1898) ; " Stream Line Motion 
of a Viscous Fluid," Report of British Association (1898). 

III. PHENOMENA OF THE DISCHARGE OF LIQUIDS FROM 
ORIFICES AS ASCERTAINABLE BY EXPERIMENTS 

§ 16. When a liquid issues vertically from a small orifice, it forms 
a jet which rises nearly to the level of the free surface of the liquid 
in the vessel from which 
it flows. The difference 
of level h, (fig. 14) is 
so small that it may be 
at once suspected to be 
due either to air resistance 
on the surface of the jet 
or to the viscosity of the 
liquid or to friction against 
the sides of the orifice. 
Neglecting for the moment 
this small quantity, we 
may infer, from the eleva- 
tion of the jet, that each 
molecule on leaving the 
orifice possessed the velo- 
city required to lift it 
against gravity to the 
height h. From ordinary 
dynamics, the relation 
between the velocity and 
height of projection is 
given by the equ ation 

V = ij2gh._ (1) 

As this velocity is nearly 
reached in the flow from 
well-formed orifices, it is 
sometimes called the theoretical velocity of discharge. This relation 
was first obtained by Torricelli. 

If the orifice is of a suitable conoidal form, the water issues in 
filaments normal to the plane of the orifice. Let o> be the area of 
the orifice, then the discharge per second must be, from eq. (1), 

Q = av = w V 2gh nearly . (2 ) 

This is sometimes quite improperly called the theoretical dis- 
charge for any kind of orifice. Except for a well-formed conoidal 
orifice the result is not approximate even, so that if it is supposed 
to be based on a theory the theory is a false one. 

Use of the term Head in Hydraulics. — The term head is an old 
millwright's term, and meant primarily the height through which a 
mass of water descended in actuating a hydraulic machine. Since 
the water in fig. 14 descends through a height h to the orifice, we 
may say there are h ft. of head above the orifice. Still more generally 
any mass of liquid h ft. above a horizontal plane may be said to have 
h ft. of elevation head relatively to that datum plane. Further, 
since the pressure p at the orifice which produces outflow is connected 
with h by the relation p/G = h, the quantity p/G may be termed 
the pressure head at the orifice. Lastly, the velocity v is connected 
with h by the relation D 2 /2g = /s, so that v 2 /2g may be termed the 
head due to the velocity v. 

§ 1 7. Coefficients of Veloc ity a nd Resistance. — As the actual velocity 
of discharge differs from V 2gh by a small quantity, let the actual 
velocity 

= V a =C v Tj2gh, (3) 

where c„ is a coefficient to be determined by experiment, called the 
coefficient of velocity. This coefficient is found to be tolerably con- 
stant for different heads with well-formed simple orifices, and it very 
often has the value 0-97. 

The difference between the velocity of discharge and the velocity 
due to the head may be reckoned in another way. The total height 
h causing outflow consists of two parts — one part h e expended 
effectively in producing the velocity of outflow, another hr in over- 
coming the resistances due to viscosity and friction. Let 

h r = C r ke, 

where c, is a coefficient determined by experiment, and called the 
coefficient of resistance of the orifice. It is tolerably constant for 
different heads with well-formed orifices. Then 




J>„ = V 2gh, = V \2gh!{\ +C r )}. 



(4) 



DISCHARGE OF LIQUIDS] 



HYDRAULICS 



39 



The relation between c» and c, for any orifice is easily found : — 

Va = C„V 2gA = V [2ghKl +C r )} 

e. = V|i/(i+*)}. (5) 

Cr=l/C„ 2 -I. (5fl) 

Thus if c, =0-97, then c r = o-o628. That is, for such an orifice about 
6j % of the head is expended in overcoming frictional resistances 
to flow. 

Coefficient of Contraction — Sharp-edged Orifices in Plane Surfaces. — 
When a jet issues from an aperture in a vessel, it may either spring 






Fig. 15. 

clear from the inner edge of the orifice as at a or & (fig. 15), or it 
may adhere to the sides of the orifice as at c. The former condition 
will be found if the orifice is bevelled outwards as at a, so as to be 
sharp edged, and it will also occur generally for a prismatic aperture 
like b, provided the thickness of the plate in which the aperture is 
formed is less than the diameter 
of the jet. But if the thickness 
is greater the condition shown 
at c will occur. 

When the discharge occurs 
as at a or b, the filaments con- 
verging towards the orifice 
continue to converge beyond 
it, so that the section of the 
jet where the filaments have 
become parallel is smaller than 
the section of the orifice. The 
inertia of the filaments opposes 
sudden change of direction 
of motion at the edge of the 
orifice, and the convergence 
continues for a distance of 
about half the diameter of the 
orifice beyond it. Let u be the 

area of the orifice, and c c a> the area of the jet at the point where 
convergence ceases; then c c is a coefficient to be determined experi- 
mentally for each kind of orifice, called the coefficient of contraction. 
When the orifice is a sharp-edged orifice in a plane surface, the 
value of c e is on the average 0-64, or the section of the jet is very 
nearly five-eighths of the area of the orifice. 

Coefficient of Discharge. — In applying the general formula Q=ui> 
to a stream, it is assumed that the filaments have a common velocity 

v normal to the section u. But if 
the jet contracts, it is at the con- 
tracted section of the jet that 
the direction of motion is normal 
to a transverse section of the 
jet. Hence the actual discharge 
when contraction occurs is 

Qo = c„z)XCcw = CcCi,wV ( 2 gh), 
or simply, if c = cc c , 

Qa = ClW(2g/l),' 

where c is called the coefficient 
of discharge. Thus for a sharp- 
edged plane orifice c = o-gjX 
o-64 = o-62. 

§ 18. Experimental Determina- 
tion of c„, c c , and c. — The co- 
efficient of contraction c c is 
directly determined by measur- 
ing the dimensions of the jet. 



the orifice, and t the time in which a particle moves from O to A, 
then 

x=v a l;y = \gP. 
Eliminating t, 

Va = <{gX i l2y). 

Then 

c v =VaH (2gh) = V (x*/4yh). 

In the case of large orifices such as weirs, the velocity can be 
directly determined by using a Pitot tube (§ 144). 

The coefficient of discharge, which for practical purposes is the 
most important of the three coefficients, is best determined by tank 
measurement of 
the flow from the 
given orifice in a 
suitable time. If 
Q is the discharge 
measured in the 
tank per second, 
then 

C=Q/<oV(2gfc). 

Measurements of 

this kind though 

simple in principle 

are not free from 

some practical 

difficulties, and 

require m uch care. 

In fig. 18 is shown 

an arrangement of 

measuring tank. 

The orifice is fixed 

in the wall of the cistern A and discharges either into the waste 

channel BB, or into the measuring tank. There is a short trough 

on rollers C which when run under the jet directs the discharge 

into the tank, and when run back again allows the discharge to drop 




Fig. 17. 




Fig. 16. 



For this purpose fixed screws of fine pitch (fig. 16) are convenient. 
These are set to touch the jet, and then the distance between them 
can be measured at leisure. 

The coefficient of velocity is determined directly by measuring 
the parabolic path of a horizontal jet. 

Let OX, OY (fig. 17) be horizontal and vertical axes, the origin 
being at the orifice. Let h be the head, and x, y the coordinates of 
a point A on the parabolic path of the jet. If j>„ is the velocity at 



into the waste channel. D is a stilling screen to prevent agitation 
of the surface at the measuring point, E, and F is a discharge valve 
for emptying the measuring tank. The rise of level in the tank, the 
time of the flow and the head over the orifice at that time must be 
exactly observed. 

For well made sharp-edged orifices, small relatively to the water 
surface in the supply reservoir, the coefficients under different 
conditions of head are pretty exactly known. Suppose the same 
quantity of water is made to flow in succession through such an 
orifice and through another orifice of which the coefficient is re- 
quired, and when the rate of flow is constant the heads over each 
orifice are noted. Let hi, fe be the heads, coi, coj the areas of the 
orifices, c\, Ci the coefficients. Then since the flow through each 
orifice is the same 

Q =CiwiV (2gfcl) =c 2 wjV (2gfe). 
c 2 = ci(wi/cu 2 ) V (hi/h). 
§ 19. Coefficients for Bellmoulhs and Bellmouthed Orifices. — If an 
orifice is furnished with a mouthpiece exactly of the form of the 



-D'l-2Sd- 



tfS*«**"'j 



0-3 D 

-OG2.5 d 



d-0-8D .— 



r 



Fig. 19. 



contracted vein, then the whole of the contraction occurs within 
the mouthpiece, and if the area of the orifice is measured at the 
smaller end, c„ must be put = i. It is often desirable to bellmouth 
the ends of pipes, to avoid the loss of head which occurs if this is 



4° 



HYDRAULICS 



[DISCHARGE OF LIQUIDS 



not done; and such a bellmouth may also have the form of the con- 
tracted jet. Fig. 19 shows the proportions of such a bellmouth 
or bellmouthed orifice, which approximates to the form of the con- 
tracted jet sufficiently for any practical purpose. 

For such an orifice L. J. Weisbach found the following values of 
the coefficients with different heads. 



Head over orifice, in ft. = h 


•66 


1-64 


11-48 


5577 


337-93 


Coefficient of velocity = c„ . 
Coefficient of resistance = c r 


•959 
•087 


•967 
•069 


•975 
•052 


•994 
•012 


•994 
•012 



As there is no contraction after the jet issues from the orifice, 
c c — I , c = c v ; and therefore 

Q =c„«V (2gh) =«V \2gh/(l +c r )}. 

§ 20. Coefficients for Sharp-edged or virtually Sharp-edged Orifices. — 
There are a very large number of measurements of discharge from 
sharp-edged orifices under different conditions of head. An account 
of these and a very careful tabulation of the average values of the 
coefficients will be found in the Hydraulics of the late Hamilton 
Smith (Wiley & Sons, New York, 1886). The following short table 
abstracted from a larger one will give a fair notion of how the co- 
efficient varies according to the most trustworthy of the experiments. 

Coefficient of Discharge for Vertical Circular Orifices, Sharp-edged, 
with free Discharge into the Air. Q = c«V (2gh). 



Head 

measured to 

Centre of 

Orifice. 



°'3 
0-4 
o-6 
0-8 
i-o 
2-0 
4-0 
8-o 

20-O 



Diameters of Orifice. 



■04 



•40 



■60 



Values of C. 



■655 
•648 
•644 
•632 
•623 
•614 
•601 



•637 
•630 
•626 
•623 
•614 
•609 
•605 
•599 



621 










618 










613 


•601 


•596 


•588 




610 


•601 


•597 


•594 


•58.3 


608 


•600 


•598 


•595 


•59i 


604 


•599 


•599 


•597 


•595 


602 


•599 


•598 


•597 


•596 


600 


•598 


•597 


•596 


•596 


596 


•596 


•596 


■596 


•594 



At the same time it must be observed that differences of sharpness 
in the edge of the orifice and some other circumstances affect the 
results, so that the values found by different careful experimenters 
are not a little discrepant. When exact measurement of flow has 
to be made by a sharp-edged orifice it is desirable that the coefficient 
for the particular orifice should be directly determined. 

The following results were obtained by Dr H. T. Bovey in the 
laboratory of McGill University. 

Coefficient of Discharge for Sharp-edged Orifices. 



Head in 
ft. 


Form of Orifice. 


Cir- 
cular. 


Square. 


Rectangular Ratio 
of Sides 4:1. 


Rectangular Ratio 
of Sides 16:1. 


Tri- 
angular. 


Sides 
vertical. 


Dia- 
gonal 
vertical. 


Long 

Sides 

vertical. 


Long 
Sides 
hori- 
zontal. 


Long 

Sides 

vertical. 


Long 
Sides 
hori- 
zontal. 


I 

2 

4 

6 

8 

10 

12 

14 
16 

18 
20 


•620 
•613 
•608 
•607 
■606 
■605 
•604 
•604 
•603 
•603 
•603 


•627 
•620 
•616 
•614 
•613 
•6l2 
•6ll 
•6lO 
•6lO 
•6l0 
•609 


■628 
•628 
•618 
•616 
•614 
•613 
•612 
•6l2 
•6ll 
•6ll 
•6ll 


•642 

•634 
•628 
■626 
•623 
■622 
•622 
•621 
•620 
•620 
•620 


•643 
•636 
•629 
•627 
•625 
•624 
•623 
•622 
•622 
•621 
•621 


•663 
•650 
■64I 
•637 
•634 
•632 
•63I 
■630 
•63O 
•630 
■629 


•664 
•6 5 I 
•642 
•637 
■635 
•633 
■631 
•630 
■630 
•629 
■628 


•636 
•628 
•623 
•620 
•619 
•618 
•618 
•618 
•617 
•616 
■616 



The orifice was 0-196 sq. in. area and the reductions were made 
with g =32- 176 the value for Montreal. The value of the coefficient 
appears to increase as (perimeter) / (area) increases. It decreases 
as the head increases. It decreases a little as the size of the orifice 
is greater. 

Very careful experiments by J. G. Mair (Proc. Inst. Civ. Eng. 
lxxxiv.) on the discharge from circular orifices gave the results 
shown on top of next column. 

The edges of the orifices were got up with scrapers to a sharp 
square edge. The coefficients generally fall as the head increases 
and as the diameter increases. Professor W. C. Unwin found that 
the results agree with the formula 

c = 0-6075 +0-0098/V h- o-ootfd, 
where h is in feet and d in inches. 



Coefficients of Discharge from Circular Orifices 
Temperature 51° to 55°. 



1 Head in 


Diameters of Orifices in Inches (d). 


feet 




















h. 


1 


ii 


1 1 


1* 


2 


ai 


2i 


2i 


3 


•75 




Coefficients (c). 




•616 


•614 


•616 


•610 


•616 


•612 


•607 


•607 


•609 


I-O 


•613 


•612 


•612 


•611 


•612 


•611 


•604 


•608 


•609 


1-25 


■613 


•614 


■610 


•608 


•612 


•608 


•605 


•60s 


■606 


I -50 


•610 


■612 


•611 


•606 


•610 


•607 


•603 


•607 


•605 


i-75 


•612 


•611 


•611 


•605 


•611 


•605 


•604 


■607 


•605 


2-00 


•609 


•613 


•609 


•606 


■609 


■606 


•604 


■604 


•605 



The following table, compiled by J. T. Fanning (Treatise on Water 
Supply Engineering), gives values for rectangular orifices in ver- 
tical plane surfaces, the head being measured, not immediately 
over the orifice, where the surface is depressed, but to the still- 
water surface at some distance from the orifice. The values were 
obtained by graphic interpolation, all the most reliable ex- 
periments being plotted and curves drawn so as to average the 
discrepancies. 

Coefficients of Discharge for Rectangular Orifices, Sharp- 
in Vertical Plane Surfaces. 



Head to 

Centre of 

Orifice. 



Ratio of Height to Width. 



Feet. 



0-2 

•3 
•4 
•5 
•6 

•7 
•8 

•9 
i-o 
1-25 
1-50 

1-75 
2 

2-25 
2-50 

2-75 

3 

3-5 

4 

4-5 

5 

6 

7 
8 

9 
10 

15 
20 

25 
30 
35 
40 

45 
50 



•6290 
•6280 
•6273 
•6250 
•6245 
•6226 
•6208 
■6158 
•6124 
•6090 
•6060 
■6035 
•6040 
•6045 
•6048 
•6054 
■6060 
•6066 
•6054 
•6086 



•6188 
•6187 
•6186 
•6183 
■6180 
•6176 

•6i73 
•6170 
•6160 
■6150 
•6138 
•6124 
•6094 
•6064 
•6036 
•6020 
•6015 
■6018 
■6024 
•6028 
•6034 
•6039 
■6045 
•6052 
•6060 



•6130 
•6134 

•6i35 
•6140 
•6144 
•6145 
•6144 
•6143 
•6139 
•6136 
•6132 
•6123 
•6110 
■6100 
•6088 
•6063 
•6038 
•6022 
•6014 
•6010 
■6010 
•6012 
•6014 
•6017 
■6021 
■6025 
•6029 
•6034 



'.3 'is 



•5984 

•5994 
•6000 
■6006 
•6010 
•6018 
•6026 
•6033 
•6036 
■6029 
•6043 
•6046 
•6048 
•6050 
•6047 
•6044 
•6038 
•6020 
•601 1 
•6010 
•6010 
•6010 
•601 1 
•6012 
•6012 
■6013 
•6014 
•6015 
•6016 
•6018 



i 



•6050 
■6063 
•6074 
•6082 
•6086 
•6090 
■6095 
■6100 
•6103 
•6104 
•6103 
•6102 
•6101 
■6100 
■6094 
•6085 
•6074 
•6063 
•6044 
•6032 
•6022 
•6015 
■6010 
•6012 
•6014 
•6016 
•6018 
•6022 
•6026 
•6030 
•6035 



6140 
6150 
6156 
6162 
6165 
6168 
6172 

6i73 
6172 
6168 
6166 
6163 
6i57 
6i55 
6i53 
6146 
6136 
6125 
6114 
6087 
6058 
6033 
6020 
6010 
6013 
6018 
6022 
6027 
6032 
6037 
6043 
6050 



23 



•6293 
•6306 
•6313 
•6317 
•6319 
•6322 
•6323 
•6320 
•6317 
•6313 
•6307 
•6302 
•6293 
•6282 
•6274 
•6267 
•6254 
•6236 
•6222 
•6202 
•6154 
•6lIO 
•6073 
•6045 
•6O30 
■6033 
•6036 
•604O 
•6044 
•6049 

•6055 
•6062 
•6070 



•6333 
•6334 
•6334 
•6333 
•6332 
•6328 
•6326 
•6324 
•6320 
■6312 
•6303 
•6296 
■6291 
■6286 
•6278 
•6273 
•6267 
•6254 
•6236 
•6222 
•6202 
•6154 
•6II4 
•6087 
•6O70 
•606O 
•6066 
•6074 
•6083 
•6092 
•6IO3 
•6II4 
•6125 
•6I4O 



§21. Orifices with Edges of Sensible Thickness. — When the edges of 
the orifice are not bevelled outwards, but have a sensible thickness, 
the coefficient of discharge is somewhat altered. The following 
table gives values of the coefficient of discharge for the arrangerrieats 
of the orifice shown in vertical section at P, Q, R (fig. 20). The 
plan of all the orifices is shown at S. The planks forming the orifice 
and sluice were each 2 in. thick, and the orifices were all 24 in. wide. 
The heads were measured immediately over the orifice. In this case, 
Q=r&(H-ft)V{2g(H+ft)/2}. 

§ 22. Partially Suppressed Contraction. — Since the contraction of 
the jet is due to the convergence towards the orifice of the issuing 
streams, it will be diminished if for any portion of the edge of the 
orifice the convergence is prevented. Thus, if an internal rim or 
border is applied to part of the edge of the orifice (fig. 21), the con- 
vergence for so much of the edge is suppressed. For such cases 
G. Bidone found the following empirical formulae applicable : — 



DISCHARGE OF LIQUIDS] 



HYDRAULICS 



4i 







Table 


of Coefficients of Discharge for Rectangular Vertical Orifices in Fig 


. 20. 






Head h 
above 
upper 
edgj oi 


Height of Orifice, H - h, in feet. 


i-3i 


0-66 


0-16 


O-IO 


Orifice 


























in feet. 


P 


Q 


R 


P 


Q 


R 


P 





R 


p 


Q 


R 


0-328 


0-598 


0-644 


0-648 


0-634 


0-665 


0-668 


0-691 


0-664 


o-666 


0-710 


0-694 


0-696 


•656 


0-609 


0-653 


0-657 


0-640 


0-672 


0-675 


0-685 


0-687 


0-688 


0-696 


0-704 


0-706 


•787 


0-612 


0-655 


0-659 


0-641 


0-674 


0-677 


0-684 


0-690 


0-692 


0-694 


0-706 


0-708 


■984 


0-616 


0-656 


o-66o 


0-641 


0-675 


0-678 


0-683 


0-693 


0-695 


0-692 


0-709 


0-711 


1-968 


0-618 


0-649 


0-653 


0-640 


0-676 


0-679 


0-678 


0-695 


0-697 


o-688 


0-710 


0-712 


3-28 


0-608 


0-632 


0-634 


0-638 


0-674 


0-676 


0-673 


0-694 


0-695 


0-680 


0-704 


0-705 


4-27 


0-602 


0-624 


0-626 


0-637 


0-673 


0-675 


0-672 


0-693 


0-694 


0-678 


0-701 


0-702 


4-92 


0-598 


0-620 


0-622 


0-637 


0-673 


0-674 


0-672 


0-692 


0-693 


0-676 


0-699 


0-699 


5-58 


0-596 


0-618 


0-620 


0-637 


0-672 


0-673 


0-672 


0-692 


0-693 


0-676 


0-698 


0-698 


6-56 


0-595 


0-615 


0-617 


0-636 


0-671 


0-672 


0-671 


0-691 


0-692 


0-675 


0-696 


0-696 


9-84 


0-592 


o-6u 


0-612 


0-634 


0-669 


0-670 


0-668 


0-689 


0-690 


0-672 


0-693 


0-693 



For rectangular orifices, 

c c =0-62(1 +o-l52«/£) ; 
and for circular orifices, 

c c = 0-62(1 -\~o-l28n/p) ; 
when n is the length of the edge of the orifice over which the border 
extends, and p is the whole length of edge or perimeter of the orifice. 
The following are the values of c c , when the border extends over 
i, J or j of the whole perimeter: — 



nip 


Cc 

Rectangular Orifices. 


Cc 

Circular Orifices. 


0-25 

0-50 

o-75 


0-643 
0-667 
0-691 


•640 
•660 
•680 



For larger values of nip the formulae are not applicable. C. R. 

Bornemann has shown, 
however, that these for- 
mulae for suppressed con- 
traction are not reliable. 

§ 23. Imperfect Con- 
traction. — If the sides of 
the vessel approach near 
to the edge of the orifice, 
they interfere with the 
convergence of the streams 
^ to which the contraction 
is due, and the contraction 
is then modified. It is 
generally stated that the 
influence of the sides 
begins to be felt if their 
distance from the edge of 
the orifice is less than 2-7 
times the corresDonding 








§ 24. Orifices Furnished with Channels of Discharge. — These ex- 
ternal borders to an orifice also modify the contraction. 

The following coefficients of discharge were obtained with open- 
ings 8 in. wide, and small in proportion to the channel of approach 
(fig. 22, A, B, C). 



ft-j— k\ in 
feet. 


h\ in feet. 


■0656 


'l64 


•328 


•656 


1-640 


3' 28 


4-92 


656 


984 


B \ 0-656 
C) 

A ) 

B \ 0-164 

c) 


•480 
■48O 

•527 
•488 
•487 
•585 


•5" 
•510 

•553 
•577 
•57i 
•614 


■542 
•538 

•574 
■624 
•606 
■633 


•574 
•506 

•592 
•631 
•617 
•645 


•599 
•592 
•607 
•625 
•626 
•652 


•601 
•600 
•610 
■624 
•628 
■651 


•601 
•602 
•610 
•619 
•627 
•650 


•601 
•602 
•609 
■613 
•623 
•650 


■601 
■601 
•608 
■606 
•618 
■649 



§ 25. Inversion of the Jet. — When a jet issues from a horizontal 
orifice, or is of small size compared with the head, it presents no 




A 




Fig. 20. 



Fig. 21. 




Fig. 23. 



width of the orifice. The coefficients of contraction for this case | marked peculiarity of form. But if the orifice is in a vertical sur- 
are imperfectly known. | face, and if its dimensions are not small compared with the head, 








_l 


*l 




h 3 

1 


.-i- 


-\- 


1 

* 







Fig. 22. 



Slope 2 in 10 

U- ■#- 4 




42 



HYDRAULICS 



[STEADY MOTION OF FLUIDS 




it undergoes a series of singular changes of form after leaving the 
orifice. These were first investigated by G. Bidone (1781-1839); 
subsequently H. G. Magnus (1802-1870) measured jets from different 
orifices; and later Lord Rayleigh {Proc. Roy. Soc. xxix. 71) in- 
vestigated them anew. 

Fig. 23 shows some forms, the upper figure giving the shape of 
the orifices, and the others sections of the jet. The jet first contracts 
as described above, in consequence of the convergence of the fluid 
streams within the vessel, retaining, however, a form similar to that 
of the orifice. Afterwards it expands into sheets in planes per- 
pendicular to the sides of the orifice. Thus the jet from a triangular 
orifice expands into three sheets, in planes bisecting at right angles 
the three sides of the triangle. Generally a jet from an orifice, in 
the form of a regular polygon of n sides, forms n sheets in planes 
perpendicular to the sides of the polygon. 

Bidone explains this by reference to the simpler case of meeting 
streams. If two equal streams having the same axis, but moving 
in opposite directions, meet, they spread out into a thin disk normal 
to the common axis of the streams. If the directions of two streams 
intersect obliquely they spread into a symmetrical sheet perpendicular 
to the plane of the streams. 

Let 01, a 2 (fig. 24) be two points in an orifice at depths hi, hi from 
the free surface. The filaments issuing at ai, 02 will have the different 

velocities V 2ghi and V 2ghi. 
Consequently they will 
tend to describe parabolic 
paths dicbi and ancbz of 
different horizontal range, 
and intersecting in the 
point c. But since two 
filaments cannot simul- 
taneously flow through the 
same point, they must 
exercise mutual pressure, 
and will be deflected out of 
the paths they tend to 
describe. It is this mutual 
pressure which causes 
the expansion of the jet 
into sheets. 

Lord Rayleigh pointed out that, when the orifices are small and 
the head is not great, the expansion of the sheets in directions per- 
pendicular to the direction of flow reaches a limit. Sections taken 
at greater distance from the orifice show a contraction of the sheets 
until a compact form is reached similar to that at the first contrac- 
tion. Beyond this point, if the jet retains its coherence, sheets are 
thrown out again, but in directions bisecting the angles between the 
previous sheets. Lord Rayleigh accepts an explanation of this con- 
traction first suggested by H. Buff (1805-1878), namely, that it is 
due to surface tension. 

§ 26. Influence of Temperature on Discharge of Orifices. — Professor 
VV. C. Unwin found {Phil. Mag., October 1878, p. 281) that for 
sharp-edged orifices temperature has a very small influence on the 
discharge. For an orifice I cm. in diameter with heads of about 
I to 1 5 ft. the coefficients were: — 

Temperature F C. 

2°5° • -594 

62 -598 

For a conoidal or bell-mouthed orifice I cm. diameter the effect of 
temperature was greater: — 

Temperature F C. 

190 0-987 

130° 0-974 

60 . 0-942 

an increase in velocity of discharge of 4% when the temperature 
increased 130 . 

J. G. Mair repeated these experiments on a much larger scale 
(Proc. Inst. Civ. Eng. lxxxiv.). For a sharp-edged orifice 2§ in. 
diameter, with a head of 1-75 ft., the coefficient was 0-604 at 57 
and 0607 at 179 F., a very small difference. With a conoidal 
orifice the coefficient was 0-961 at 55 and 0-981 at 170 F. The 
corresponding coefficients of resistance are 0-0828 and 0-0391, 
showing that the resistance decreases to about half at the higher 
temperature. 

§ 27. Fire Hose Nozzles. — Experiments have been made by J. R. 
Freeman on the coefficient of discharge from smooth cone nozzles 
used for fire purposes. The coefficient was found to be 0-983 for f-in 



Fig. 24. 



82 for 



in. 



0-972 for 1 in.; 0-976 for if in.; and 



open channel, for instance, when the effect of eddies produced by the 
roughness of the sides is neglected, the pressure at each point is 
simply the hydrostatic pressure due to the depth below the free 
surface. 

(6) If the velocity of the fluid is very small, the distribution of 
pressure is approximately the same as in a fluid at rest. 

(c) If the fluid molecules take precisely the accelerations which 
they would have if independent and submitted only to the external 
forces, the pressure is uniform. Thus in a jet falling freely in the 
air the pressure throughout any cross section is uniform and equal 
to the atmospheric pressure. 

(d) In any bounded plane section traversed normally by streams 
which are rectilinear for a certain distance on either side of the 
section, the distribution of pressure is the same as in a fluid at rest. 

Distribution of Energy in Incompressible Fluids. 

§ 29. Application of the Principle of the Conservation of Energy to 
Cases of Stream Line Motion. — The external and internal work 
done on a mass is equal to the change of kinetic energy produced. 
In many hydraulic questions this principle is difficult to apply, be- 
cause from the complicated nature of the motion produced it is 
difficult to estimate the total kinetic energy generated, and because 
in some cases the internal work done in overcoming frictional or 
viscous resistances cannot be ascertained ; but in the case of stream 
line motion it furnishes a simple and important result known as 
Bernoulli's theorem. 

Let AB (fig. 25) be any one elementary stream, in a steadily moving 
fluid mass. Then, from the steadiness of the motion, AB is a fixed 
path in space through which a stream of fluid is constantly flowing. 
Let 00 be the free surface and XX any horizontal datum line. Let 

o o 



nozzle ; o 

097 1 for 1} in. The nozzles were fixed on a taper play-pipe, and the 
coefficient includes the resistance of this pipe (Amer. Soc. Civ. Eng. 
xxi.. 1889). Other forms of nozzle were tried such as ring nozzles 
for which the coefficient was smaller. 

IV. THEORY OF THE STEADY MOTION OF FLUIDS. 

§ 28. The general equation of the steady motion of a fluid given 
under Hydrodynamics furnishes immediately three results as to the 
distribution of pressure in a stream which may here be assumed. 

(a) If the motion is rectilinear and uniform, the variation of 
pressure is the same as in a fluid at rest. In a stream flowing in an 




Fig. 25. 

w be the area of a normal cross section, v the velocity, p the intensity 
of pressure, and 2 the elevation above XX, of the elementary stream 
AB at A, and o>i, pi, Vi, 21 the same quantities at B. Suppose that 
in a short time t the mass of fluid initially occupying AB comes to 
A'B'. Then AA', BB' are equal to vt, Vit, and the volumes of fluid 
AA', BB' are the equal inflow and outflow = Qt = uvt = uiVit, in the 
given time. If we suppose the filament AB surrounded by other 
filaments moving with not very different velocities, the frictional 
or viscous resistance on its surface will be small enough to 
be neglected, and if the fluid is incompressible no internal work is 
done in change of volume. Then the work done by external forces 
will be equal to the kinetic energy produced in the time considered. 
The normal pressures on the surface of the mass (excluding the 
ends A, B) are at each point normal to the direction of motion, and 
do no work. Hence the only external forces to be reckoned are 
gravity and the pressures on the ends of the stream. 

The work of gravity when AB falls to A'B' is the same as that of 
transferring AA' to BB'; that is, GQt (z—Zi). The work of the 
pressures on the ends, reckoning that at B negative, because it is 
opposite to the direction of motion, is (puiy.vt) — (piuiXvit) = 
Qt{p—pi). The change of kinetic energy in the time / is the differ- 
ence of the kinetic energy originally possessed by AA' and that 
finally acquired by BB', for in the intermediate part A'B there is 
no change of kinetic energy, in consequence of the steadiness of the 
motion. But the mass of AA' and BB' is GQt/g, and the change of 
kinetic energy is therefore (GQ//g) (z>i 2 /2 — 1> 2 /2). Equating this to the 
work done on the mass AB, 

GQt(z- Zl )+Qt(p-Pi) = (GQt/g)Wl2-vV2). 
Dividing by GQt and rearranging the terms, 

vV2g+plG+z=v 1 -/2g+p 1 IG+z 1 ; (1) 

or, as A and B are any two points, 

» 2 /2g+p/G-r-3=constant = H. _ (2) 

Now n 2 /2g is the head due to the velocity v, pjG is the head equivalent 
to the pressure, and 2 is the elevation above the datum (see § 16). 
Hence the terms on the left are the total head due to velocity, 
pressure, and elevation at a given cross section of the filament, 2 is 
easily seen to be the work in foot-pounds which would be done 
by I lb of fluid falling to the datum line, and similarly pjG and 
i> 2 /2g are the quantities of work which would be done by I lb of fluid 
due to the pressure p and velocity v. The expression on the left of 
the equation is, therefore, the total energy of the stream at the 
section considered, per lb of fluid, estimated with reference to the 



STEADY MOTION OF FLUIDS] 

datum line XX. Hence we see that in stream line motion, under 
the restrictions named above, the total energy per lb of fluid is 
uniformly distributed along the stream line. If the free surface of 
the fluid 00 is taken as the datum, and -h, -hi are the depths of A 
and a measured down from the free surface, the equation takes the 
form 

^/2g+plG-h=v 1 */2g+p l /G-h l ; (,) 

or generally 

i' 2 /2£ +p/G — h = constant . ( 3 o) 

§ 30. Second Form of the Theorem of Bernoulli.— Suppose at the 
two sections A, B (fig. 26) of an elementary stream small vertical 
pipes are introduced, which may be termed pressure columns 



HYDRAULICS 




4-3 

projected surface as HI, and the pressures parallel to the axis of 
the pipe, normal to these projected surfaces, balance each other 
Similarly the pressures on BC, CD balance those on GH, EG In 
the same way, in any combination of enlargements and contrac- 
tions, a balance of pressures, due to the flow of liquid parallel to the 



^^^ 





~-~-^Y ~ "~ 


a~ 


1 




— )• 




, 




1 




H 

1 




1 





-vl 



'? 







Fig. 26. 

(I 8), having their lower ends accurately parallel to the direction of 
flew. In such tubes the water will rise to heights corresponding to 
the pressures at A and B. Hence b = p/G, and b'=p,/G. Conse- 
quently the tops of the pressure columns A' and B' will be at 
total heights b -\ c=p/G+z and b'+c' = p l /G+z 1 above the datum 
line XX. Ihe difference of level of the pressure column tops, or 
the fall of free surface level between A and B, is therefore 

. S = (i>-£i)/G + (z-z,); 
and this by equation (1), § 29 is (i^-i^g. That is, the fall of 
free surface level between two sections is equal to the difference 
of the heights due to the velocities at the sections. The line A'B' 
is sometimes called the line of hydraulic gradient, though this 
term is also used in cases where friction needs to be taken into 
account. It is the line the height of which above datum is the 
sum of the elevation and pressure head at that point, and it falls 
below a horizontal line A"B" drawn at H ft. above XX by the 
quantities a=t' 2 /2g and a' =vi 2 /2g, when friction is absent. 

§ 31. Illustrations of the Theorem of Bernoulli. In a lecture to 
the mechanical section of the British Association in 1875, W. Fronde 
gave some experimental illustrations of the principle of Bernoulli. 
He remarked that it was a common but erroneous impression that 
a fluid exercises in a contracting pipe A (fig. 27) an excess of pressure 
against the entire converging surface 
which it meets, and that, conversely, 
as it enters an enlargement B, a relief 
of pressure is experienced by the 
entire diverging surface of the' pipe. 
Further it is commonly assumed that 
when passing through a contraction 
C, there is in the narrow neck an 
excess of pressure due to the squeezing together of the liquid at that 
point. These impressions are in no respect correct; the pressure 
is smaller as the section of the pipe is smaller and conversely. 

Fig. 28 shows a pipe so formed that a contraction is followed by 
an enlargement, and fig. 29 one in which an enlargement is followed 

by a contraction. The 

A B vertical pressure columns 

show the decrease of 
pressure at the contrac- 
tion and increase of 
pressure at the enlarge- 
ment. The line 06c in 
both figures shows the 
variation of free surface 
level, supposing the pipe 
frictionless. In actual 
pipes, however, work is 
expended in friction 
..,,,,..., . , against the pipe; the 

total head diminishes in proceeding along the pipe, and the free 
surface level is a line such as ahc u falling below abc. 

Froude further pointed out that, if a pipe contracts and enlarges 
again to the same size, the resultant pressure on the converging part 
exactly balances the resultant pressure on the diverging part so 
that there is no tendency to move the pipe bodily when water flows 
through it. Thus the conical part AB (fig. 30) presents the same 



axis of the pipe, will be found, provided the sectional area and 
direction of the ends are the same. 

The following experiment is interesting. Two cisterns provided 
with converging pipes were placed so that the jet from one was ex- 
actly opposite the entrance to the other. The cisterns being filled 

-0- „ 




Fig. 29. 



very nearly to the same level, the jet from the left-hand cistern A 
entered the right-hand cistern B (fig. 31), shooting across the free 
space between them without any waste, except that due to indirect- 
ness of aim and want of exact correspondence in the form of the 
onhces. In the actual experiment there was 18 in. of head in the 
right and 2o| in. of head in the left-hand cistern, so that about 





Fig. 27. 



Fig. 30. 

2| in. were wasted in friction. It will be seen that in the open space 
between the orifices there was no pressure, except the atmospheric 
pressure acting uniformly throughout the system. 

§ 32- Ventur-- Meter.— An ingenious application of the variation 
oi pressure a-.d velocity in a converging and diverging pipe has been 




Fig. 31. 



made by Clemens Herschel in the construction of what he terms a 
Ventun Meter for measuring the flow in water mains. Suppose that, 
as in ng. 32, a contraction is made in a water main, the change of 
section being gradual to avoid the production of eddies. The ratio p 



44 



HYDRAULICS 



[STEADY MOTION OF FLUIDS 



of the cross sections at A and B, that is at inlet and throat, is in 
actual meters 5 to I to 20 to I , and is very carefully determined by 
the maker of the meter. Then, if v and u are the velocities at A 
and B, -u — pv. Let pressure pipes be introduced at A, B and C, 

8 




and let Hi, H, H2 be the pressure heads at those points. Since the 
velocity at B is greater than at A the pressure will be less. Neglect- 
ing friction 

Hi+P 2 /2g = H+K 2 /2g, 
Hi-H = (u^u-)l2g = <J>*-l)v*/2g. 

Let h = Hi-H be termed the Venturi head, then 

M = V!p 2 .2g/*/(p--l)j, 

from which the velocity through the throat and the discharge of the 
main can be calculated if the areas at A and B are known and h 
observed. Thus if the diameters at A and B are 4 and 12 in., the 
areas are 12-57 an d 113-1 sq. in., and p = 9, 

m = V8i/8oV (2gft) = i-007V (2gh). 
If the observed Venturi head is 12 ft., 

m = 28 ft. per sec, 
and the discharge of the main is 

28X12-57=351 cub. ft. per sec. 
Hence by a simple observation of pressure difference, the flow in 
the main -at any moment can be determined. Notice that the 
pressure height at C will be the same as at A except for a small loss 
hf due to friction and eddying between A and B. To get the pressure 
at the throat very exactly Herschel surrounds it by an annular 
passage communicating with the throat by several small holes, 
sometimes formed in vulcanite to prevent corrosion. Though con- 
structed to prevent eddying as much as possijle there is some eddy 
loss The main effect of this is to cause a loss of head between A 
and C which may vary from a fraction of a foot to perhaps 5 ft. 
at the highest velocities at which a meter can be used. The eddying 
also affects a little the Venturi head h. Consequently an experi- 
mental coefficient must be determined for each meter by tank measure- 
ment. The range of this coefficient is, however, surprisingly small. 
If to allow for friction, u = k\j |p 2 /(p 2 -i))v (2gh), then Herschel 
found values of k from 0-97 to i-o for throat velocities varying from 

8 to 28 ft. per sec. The 
meter is extremely con- 
venient. At Staines reser- 
voirs there are two meters 
of this type on mains 94 in. 
in diameter. Herschel con- 
trived a recording arrange- 
ment which records the 
variation of flow from hour 
to hour and also the total 
flow in any g ; ven time. In 
Great Britain Jie meter is 
constructed by 3. Kent, 
who has made improvements 
in the recording arrange- 
ment. 

In the Deacon Waste 
Water Meter (fig. 33) a 
different principle is used. 
A disk D, partly counter- 
balanced by a weight, is 
suspended in the water flow- 
ing through the main in a 
conical chamber. The un- 
balanced weight of the disk 
is supported by the impact 
of the water. If the discharge of the main increases the disk rises, but 
as it rises its position in the chamber is such that in consequence of 
the larger area the velocity is less. It finds, therefore, a new position 
of equilibrium. A pencil P records on a drum moved by clockwork 
the position of the disk, and from this the variation of flow is in- 
ferred. 

§ 33. Pressure, Velocity and Energy in Different Stream Lines.— 
The equation of Bernoulli gives the variation of pressure and velocity 



Outlet 




from point to point along a stream line, and shows that the total 
energy of the flow across any two sections is the same. Two other 
directions may be defined, one normal to the stream line and in 
the plane containing its radius of curvature at any point, the other 
normal to the stream line and the radius of curvature. For the 
problems most practically useful it will be sufficient to consider 
the stream lines as parallel to a vertical or horizontal plane. If the 
motion is in a vertical plane, the action of gravity must be taken 
into the reckoning ; if the motion is in a horizontal plane, the terms 
expressing variation of elevation of the filament will disappear. 1 

Let AB, CD (fig. 34) be two consecutive stream lines, at present 
assumed to be in a vertical plane, and PQ a normal to these lines 



j»dp 



A 



- P: 




■v*d\r 



But 



(1) 



Fig. 34. 

making an angle <#> with the vertical. Let P, Q be two particles 
moving along these lines at a distance PQ = ds, and let z be the 
height of Q above the horizontal plane with reference to which the 
energy is measured, v its velocity, and p its pressure. Then, if H is 
the total energy at Q per unit of weight of fluid, 

n=z+p/G+v 2 /2 S . 

Differentiating, we get 

dH=ds+dp/G+vdv/g, 
for the increment of energy between Q and P. 
dz — PQ cos <j> = ds cos 4> \ 
.'.dH^dp/G+vdv/g+ds cos 0, (ia) 

where the last term disappears if the motion is in a horizontal plane. 
Now imagine a small cylinder of section w described round PQ 
as an axis. This will be in equilibrium under the action of its 
centrifugal force, its weight and the pressure on its ends. But its 
volume is cods and its weight Gads. Hence, taking the components 
of the forces parallel to PQ — 

o>dp = Gv 2 oids/gp-Gui cos <pds, 
where p is the radius of curvature of the stream line at Q. Conse- 
quently, introducing these values in (1), 

dH. = vHs/gp +vdv/g = (v/g) (vfp -\-dv/ds)ds. (2) 

Currents 
§ 34. Rectilinear Current. — Suppose the motion is in parallel 
straight stream lines (fig. 35) in a vertical plane. Then p is infinite, 
and from eq. (2), § 33, 

dH = vdvjg. 
Comparing this with (1) we see that 

dz+dp/G<=o; 

.'. z-\-p/G= constant; (3) 

or the pressure varies hydrostatically as in a fluid at rest. For two 
stream lines in a horizontal D 



plane, z is constant, and there- 
fore p is constant. 

Radiating Current. — Suppose 
water flowing radially between 
horizontal parallel planes, at 
a distance apart = 5. Conceive 
two cylindrical sections of the 
current at radii n and ri, where 



-e- 
1 
1 
1 
1 

-e- 



1 

I 

■!■ ,. 



Fig. 35. 



the velocities are Vi and V2, and the pressures pi and pi. Since the 
flow across each cylindrical section of the current is the same, 
Q = 2wriSvi = 2wnSv2 
r\Vi—riVt 
ri/r 2 = K 2 /»i. (4) 

1 The following theorem is taken from a paper by J. H. Cotterill, 
" On the Distribution of Energy in a Mass of Fluid in Steady Motion," 
Phil. Mag., February 1876. 



STEADY MOTION OF FLUIDS] 



HYDRAULICS 



4.5 



The velocity would be infinite at radius o, if the current could be 
conceived to extend to the axis. Now, if the motion is steady, 



H = />i/G +Kr/2g = pzfG +v 2 2 /2g ; 

= ptlG+nWlrf2g; 
(&-£i)/G=i', 2 (i-n7>Y ! )/2g; 



(5) 

(6) 



Hence the pressure increases from the interior outwards, in a way 
indicated by the pressure columns in fig. 36, the curve through the 
free surfaces of the pressure columns being, in a radial section, the 
quasi-hyperbola of the form xy l = c z . This curve is asymptotic to a 
horizontal line, H ft. above the line from which the pressures are 
measured, and to the axis of the current. 

Free Circular Vortex. — A free circular vortex is a revolving mass 
){ water, in which the stream lines are concentric circles, and in which 




Fig. 36. 

the total head for each stream line is the same. Hence, if by any 
slow radial motion portions of the water strayed from one stream 
line to another, they would take freely the velocities propei to their' 
new positions under the action of the existing fluid pressures only. 
For such a current, the motion being horizontal, we have for all 
the circular elementary streams ] 



H = p/G+v 2 /2g = constant; 
\dH = dp/G -\-vdvjg = o. 



(7) 



pressure increasing according to the law stated above, and the head 
along each spiral stream line is constant. 

§ 35. Forced Vortex. — If the law of motion in a rotating current is 
different from that in a free vortex, some force must be applied to 
cause the variation of velocity. The simplest case is that of a 
rotating current in which all the particles have equal angular velocity, 
as for instance when they are driven round by radiating paddles 
revolving uniformly. Then in equation (2), § 33, considering two 
circular stream lines of radii r and r-\-dr (fig. 37), we have p = r, 
ds = dr. If the angular velocity is a, then v = ar and dv = adr. Hence 

dH — a. 2 rdrjg-{-a-rdrlg = 2tt.' 1 rdrlg. 
Comparing this with (1), § 33, and putting <fe = o, because the motion 
is horizontal, 

dp/G + a?rdrlg = 2 a-rdr/g, 
dp/G = a-rdr/g, 
pIG =aV / '2 g+ constant. (9) 

Let pi, n, »i be the pressure, radius and velocity of one cylindrical 
section, p 2 , r 2 , v 2 those of another; then 

pi/G-a"ri i /2g = pilG-a-r^l 2g ; 
(ft-?i)/G=a'(r 2 2 -r, 2 )/2g = (- 1 ^^)/2g. (10) 

That is, the pressure increases from within outwards in a curve 



Consider two stream lines at radii r and r+dr (fig. 36). Then in 
(■2). § 33. P*=r and ds = dr, 

Mr I gr +vdv I g = o, 
dv/v = -dr/r, 

v r i/r, _ _ (8) 

precisely as in a radiating current; and hence the distribution 
of pressure is the same, and formulae 5 and 6 are applicable to this 
case. 

Free Spiral Vortex. — As in a radiating and circular current the 
equations of motion are the same, they will also apply to a vortex 
in which the motion is compounded of these motions in any pro- 
portions, provided the radial component of the motion varies in- 
versely as the radius as in a radial current, and the tangential 
component varies inversely as the radius as in a free vortex. Then 
the whole velocity at any point will be inversely proportional to 
the radius of the point, and the fluid will describe stream lines 
having a constant inclination to the radius drawn to the axis of tie 
current. That is, the stream lines will be logarithmic spirals. 
When water is delivered from the circumference of a centrifugal 
pump or turbine into a chamber, it forms a free vortex of this kind. 
The water flows spirally outwards, its velocity diminishing and its 



\] 






-■-*-h 




! !\ 












: = 


\ 


v° 2 


- : 


K 


1 
1 
\ 




1 


J 


^m ^m 





: 1 

A I 

q I ■ ■■ 



.il 




Fig. 37. 

which in radial sections is a parabola, and surfaces of equal pressure 
are paraboloids of revolution (iig. 37). 

Dissipation of Head in Shock 
§ 36. Relation of Pressure and Velocity in a Stream in Steady 
Motion when the Changes of Section of the Stream are Abrupt. — 
When a stream changes section abruptly, rotating eddies are formed 
which dissipate energy. The energy absorbed in producing rotation 
is at once abstracted from that effective in causing the flow, and 
sooner or later it is wasted by frictional resistances due to the rapid 
relative motion of the eddying parts of the fluid. In such cases the 
work thus expended internally in the fluid is too important to be 
neglected, and the energy thus lost is commonly termed energy lost 
in shock. Suppose fig. 38 to represent a stream having such an 
abrupt change of section. Let AB, CD be normal sections at points 
where ordinary stream line motion has not been disturbed and 
where it has been re-established. Let w, p, v be the area of section, 
pressure and velocity at AB, and an, pi, v s corresponding quantities 
at CD. Then if no work were expended internally, and assuming 
the stream horizontal, we should have 

P/G+v>/2g = p i /G+v 1 '/2g. (1) 



4 6 



HYDRAULICS 



[DISCHARGE FROM ORIFICES 




Fig. 38. 



DUf 



But if work is expended in producing irregular eddying motion, the 
head at the section CD will be diminished. 

Suppose the mass ABCD comes in a short time t to A'B'C'D'. 
The resultant force parallel to the axis of the stream is 

pill +/>o(wi-w)— pltAl, 

where p is put for the unknown pressure on the annular space 
between AB and EF. The impulse of that force is 

\P"+Po("i-")-pi^\)t. 
I he horizontal change of momentum in the same time is the differ- 

_ _. ence of the momenta of 

- £ -^ pCDC'D' and ABA'B', 

. because the amount 
of momentum be- 
tween A'B' and CD 
remains unchanged 
if the motion is 
steady. The volume 
of ABA'B' or CDC'D', 
being the inflow and 
outflow in the time 
t, is Qt = owt = aiVit, 
and the momentum of 
these masses is 
(G/g)QvUnd(Glg)Qv 1 t. 
lhe change of mo- 
mentum is therefore (G/g)Qt(vi-v). Equating this to the impulse, 

{pu+M-*i-«>)-pi<'>i)t = (G/g)Q/(»i-»). 
Assume that po = p, the pressure at AB extending unchanged through 
the portions of fluid in contact with AE, BF which lie out of the 
path of the stream. Then (since Q=wifi) 

(£-£i) = (G/g)i>i(i'i-tO; 
P/G-p l /G=v l (vi-n)lg; (2) 

p/G+v i l2 S = p 1 IG+v 1 y2g+(v-v i yi2g. (3) 

This differs from the expression (1), § 29, obtained for cases where 
no sensible internal work is done, by the last term on the right. 
That is, (»-z>i) 2 /2g has to be added to the total head at CD, which 
is pi!'G+Vi*/2g, to make it equal to the total head at AB, or {v-^i) 2 /2g 
is the head lost in shock at the abrupt change of section. But 
r-i'i is the relative velocity of the two parts of the stream. Hence, 
when an abrupt change of section occurs, the head due to the relative 
velocity is lost in shock, or (i>-»i) 2 /2g foot-pounds of energy is 
wasted for each pound of fluid. Experiment verifies this result, 
so that the assumption that po = p appears to be admissible. 
If there is no shock, 

pilG=p/G + (v 2 ^)l3g. 
It there is shock, 

PiiG = £/G-t>i (»r-»)/g. 

Hence the pressure head at CD in the second case is less than in the 
former by the quantity (v-viffeg, or, putting o>iVi=uv, by the 
quantity 

(t' 2 /2g)(l-o>/ Ul ) 2 . (4) 

V. THEORY OF THE DISCHARGE FROM ORIFICES AND 
MOUTHPIECES 
§ 37. Minimum Coefficient of Contraction. Re-entrant Mouth- 
piece of Borda. — In one special case the coefficient of contraction 

can be determined 
theoretically, and, as 
it is the case where 
the convergence of the 
streams approaching 
the orifice takes place 
through the greatest 
possible angle, the co- 
efficient thus deter- 
mined is the minimum 
coefficient. 

Let fig. 39 represent 
a vessel with vertical 
sides, 00 being the 
free water surface, at 
which the pressure is 
pa. Suppose the liquid 
issues by a horizontal 
mouthpiece, which is 
re-entrant and of the 
greatest length which 
permits the jet to 
spring clear from the 
inner end of the 
orifice, without adher- 
ing to its sides. With 
such an orifice the 
velocity near the 
points CD is negligible, 
and the pressure at those points may be taken equal to the hydro- 
static pressure due to the depth from the free surface. Let S2 be 
the area of the mouthpiece AB, w that of the contracted jet aa 




Fig. 39. 



Suppose that in a short time /, the mass OOaa comes to the position 
O'O' a'a'; the impulse of the horizontal external forces acting on 
the mass during that time is equal to the horizontal change of 
momentum. 

The pressure on the side OC of the mass will be balanced by the 
pressure on the opposite side OE, and so for all other portions of the 
vertical surfaces of the mass, excepting the portion EF opposite the 
mouthpiece and the surface AaoB of the jet. On EF the pressure is 
simply the hydrostatic pressure due to the depth, that is, (p a +Gh)Q. 
On the surface and section AaaB of the jet, the horizontal resultant 
of the pressure is equal to the atmospheric pressure pa acting on the 
vertical projection AB of the jet; that is, the resultant pressure is 
-paQ. Hence the resultant horizontal force for the whole mass 
OOaa is (p a +Gh)p-pail = Ghii. Its impulse in the time / is GhSl t. 
Since the motion is steady there is no change of momentum between 
O'O' and aa. The change of horizontal momentum is, therefore, 
the difference of the horizontal momentum lost in the space OOO'O' 
and gained in the space aaa'a'. In the former space there is no 
horizontal momentum. 

The volume of the space aaa'a' is uvt; the mass of liquid in that 
space is (Glg)arvt; its momentum is (G/g)«i/ 2 /. Equating impulse to 
momentum gained, 

Gto = (G/g)utft; 
.'. »/Q = gh/v 2 . 
But u 2 = 2gh, and a/Q = c c ; 

.'.a}/Q = i=c c ; 

a result confirmed by experiment with mouthpieces of this kind. 
A similar theoretical investigation is not possible for orifices in 
plane surfaces, because the velocity along the sides of the vessel in 
the neighbourhood of the orifice is not so small that it can be 
neglected. The resultant horizontal pressure is therefore greater 
than Ghil, and the contraction is less. The experimental values of the 
coefficient of discharge for a re-entrant mouthpiece are 0-5149 
(Borda), 0-5547 (Bidone), 0-5324 (Weisbach), values which differ 
little from the theoretical value, 0-5, given above. 

§ 38. Velocity of Filaments issuing in a Jet. — A jet is composed 
of fluid filaments or elementary streams, which start into motion at 
some point in the 
interior of the vessel 
from which the fluid 
is discharged, and 
gradually acquire 
the velocity of the 
jet. Let Mot, fig. 
40 be such a fila- 
ment, the point M 
being taken where 
the velocity is in- 
sensibly small, and 
m at the most con- 
tracted section of 
the jet, where the 
filaments have be- 
come parallel and 
exercise uniform mutual pressure. Take the free surface AB for 
datum line, and let pi, i'i, hi, be the pressure, velocity and depth 
below datum at M; p, v, h, the corresponding quantities at m. 
Then § 29, eq. (3a), 

vJfrg+pilG-hi^ffeg+plG-h. (1) 

But at M, since the velocity is insensible, the pressure is the hydro- 
static pressure due to the depth'; that is, »i=o, pi=p a -\-Ghi. At 
m, p — pa, the atmospheric pressure round the jet. Hence, inserting 
these values, 

o+palG+hi-h=&l2g+palG-k ; 

vV2g = h; (2) 

or ti = V (2g/i)= 8-025 V A. (2a) 

That is, neglecting the viscosity of the fluid, the velocity of fila- 
ments at the contracted section of the jet is simply the velocity due 
to the difference of level 
of the free surface in the 
reservoir and the orifice. 
If the orifice is small in 
dimensions compared with 
h, the filaments will all 
have nearly the same vel- 
ocity, and if h is measured 
to the centre of the orifice, 
the equation above gives 
the mean velocity of the 
jet. 

Case of a Submerged 
Orifice. — Let the orifice 
discharge below the level 
of the tail water. Then 




Fig. 40. 




Fig. 



4i- 



using the notation shown in fig. 41, we have at M, Vi = o,pi = Gh;+p. 
at m, p = Gh 3 +pa. Inserting these values in (3), § 29, 

o+hi+ptlG-h^ifi/ag+hx-hi+palG; 

v 2 /2g = h r h2 = k. (3) 



DISCHARGE FROM ORIFICES] 



HYDRAULICS 



47 




where h is the difference of level of the head and tail water, and may 

be termed the effective head producing flow. 

Case where the Pressures are different on the Free Surface and at 

the Orifice.— -Let the 
fluid flow from a vessel 
in which the pressure 
is pa into a vessel in 
which the pressure is 
p, fig. 42. The pres- 
sure po will produce the 
same effect as a layer 
of fluid of thickness 
po/G added to the head 
water; and the pres- 
sure p , will produce 
the same effect as a 
layer of thickness pjG 
added to the tail 
water. Hence the 
effective difference of 
level, or effective head 
producing flow, will 
be 

h = ho+p IG-p/G; 
and the velocity of discharge will be 

f = V[2g{fc>+0-£)/Gi]. (4) 

We may express this result by saying that differences of pressure at 
the free surface and at the orifice are to be reckoned as part of the 
effective head. 

Hence in all cases thus far treated the velocity of the jet is the 
velocity due to the effective head, and the discharge, allowing for 
contraction of the jet, is 

Q=OM=Cuyl(2gh), (5) 

where « is the area of the orifice, co> the area of the contracted 
section of the jet, and h the effective head measured to the centre of 
the orifice. If h and 01 are taken in feet, Q is in cubic feet per second. 

It is obvious, however, that this formula assumes that all the 
filaments have sensibly the same velocity. That will be true for 
horizontal orifices, and very approximately true in other cases, if 
the dimensions of the orifice are not large compared with the head h. 
In large orifices in say a vertical surface, the value of h is different 
for different filaments, and then the velocity of different filaments is 
not sensibly the same. 

Simple Orifices — Head Constant 
§ 39. Large Rectangular Jets from Orifices in Vertical Plane Sur- 
faces. — Let an orifice in a vertical plane surface be so formed that it 

produces a jet having 
A B\ a rectangular con- 

tracted section with 
vertical and horizon- 
tal sides. Let b (fig. 
43) be the breadth of 
the jet, hi and fe the 
depths below the free 
surface of its upper 
and lower surfaces. 
Consider a lamina of 
the jet between the 
depths h and h+dh. 
Its normal section is 
bdh, and the velocity 
of discharge -^2gh. 
The discharge pet 




Fig. 43. 



second in this lamina 
jet is therefore 



therefore b^2gh dh, and that of the whole 



Q=/£w(2«ft)<ft 



PV2g 



'-hS 



(°) 



where the first factor on the right is a coefficient depending on the 
form of the orifice. 

Now an orifice producing a rectangular jet must itself be very 
approximately rectangular. Let B be the breadth, Hi, H 2 , the 
depths to the upper and lower edges of the orifice. Put 

6(*2 g -Ai ? )/B(H 2 2-H 1 ')=c. ( 7 ) 

Then the discharge, in terms of the dimensions of the orifice, instead 
of those of the jet, is 

Q = fcBV^(H^-H 1 ?), (8) 

the formula commonly given for the discharge of rectangular orifices. 
The coefficient c is not, however, simply the coefficient of contraction, 
the value of which is 

&(fe-W/B(H 2 -Hi), 

and not that given in (7). It cannot be assumed, therefore, that c 

in equation (8) is constant, and in fact it is found to vary for different 

values of B/H 2 and B/Hi, and must be ascertained experimentally. 

Relation between the Expressions (5) and (8). — For a rectangular 



orifice the area of the orifice is u = B (H 2 - Hi) , and the depth measured 
to its centre is J(H 2 +Hi). Putting these values in (%), 
v ™ u ,- u Q'=eB(H»-Hi)V{g(H,+H 1 )|. 
b rom (8) the discharge is 

, , Q 2 = |cBV2l(H 2 ?-H,?). 

Hence, for the same value of c in the two cases, 
t iTrt, Qs/Qi = ^ H23 - Hl8 M( H *- H 0V|(H 2 +Hi)/2}]. 
Let Hi/H 2 = <r, then 

Q2/Q1 =0-9427 (l-<r?)/[l- W(l+<r)!. (9) 

If Hi varies from o to 00 , <r( = Hi/H 2 ) varies from o to 1. The 
following table gives values of the two estimates of the discharge 
for different values of <r : — 



Hi/H 2 =<r. 


Q2/Q1. 


Hi/H 2 = <r. 


Q2/Q1. 


0-0 
0-2 

o-5 
07 


•943 
•979 
•995 
•998 


o-8 
0-9 

1-0 


•999 
•999 

1-000 



_ Hence it is obvious that, except for very small values of a, the 
simpler equation (5) gives values sensibly identical with those of 
(8). When <r<o-5 it is better to use equation (8) with values of 
c determined experimentally for the particular proportions of orifice 
which are in question. 

§ 40. Large Jets having a Circular Section from Orifices in a Vertical 
Plane Surface. — Let fig. 44 represent the section of the jet, 00 being 
O o 




Fig. 44. 
the free surface level in the reservoir. The discharge through the 
horizontal strip aabb, of breadth aa = b, between the depths hi-\-y 
and h-jry+dy, is 

ti, t. 1 a- u , d g=.Wj2«(*i+y))<*y. 
I he whole discharge of the jet is 

Q=J\i{2g(hi+y)}dy. 

But6=rfsin0; y = |i(i -cos <j>) ; dy = \d sin <j> d<t>. Let e = d/(2ki+d), 
then 

Q = i<Z 2 V \2g(hi+dl2)}( "sin 2 0\'i-ecos0<Z4>. 

From eq. (5), putting co = «P/4, h = hi+dJ2, c = i when d is the 
diameter of the jet and not that of the orifice, 

Qi = i^y|2g(Ai+<J/a)}, 

Q/Qi=2/?rJ sin 2 <#>V {1— ecos 4>\d<f,. 

For hi = 00 , e = o and Q/Qi = 1 ; 

and for hi=o, e = i and Q/Qi =0-96. 

So that in this case also the difference between the simple formula 
(5) and the formula above, in which the variation of head at different 
parts of the orifice is taken into account, is very small. 

Notches and Weirs 
§ 41. Notches, Weirs and Eyewashes. — A notch is an orifice ex- 
tending up to the free surface level in the reservoir from which the 
discharge takes place. A weir is a structure over which the water 
flows, the discharge being in the same conditions as for a notch. 
The formula of discharge for an orifice of this kind is ordinarily 
deduced by putting Hi =0 in the formula for the corresponding orifice, 
obtained as in the preceding section. Thus for a rectangular notch, 
put H!=oin (8). Then 

Q = !cBV(2g)H?, (11) 

where H is put for the depth to the crest of the weir or the bottom 
of the notch. Fig. 45 shows the mode in which the discharge occurs 
in the case of a rectangular notch or weir with a level crest. As. the 
free surface level falls very sensibly near the notch, the head H 
should be measured at some distance back from the notch, at a 
point where the velocity of the water is very small. 

Since the area of the notch opening is BH, the above formula is 
of the form 

Q=eXBHXfeV(2gH), 
where Hs a factor depending on the form of the notch and expressing 
the ratio of the mean velocity of discharge to the velocity due to the 
depth H. 

§ 42. Francis's Formula for Rectangular Notches. — The jet dis- 
charged through a rectangular notch has a section smaller than BH, 
(a) because of the fall of the water surface from the point where H 



4 8 



HYDRAULICS 



[DISCHARGE FROM ORIFICES 



is measured towards the weir, (6) in consequence of the crest con- 
traction, (c) in consequence of the end contractions. It may be 
pointed out that while the diminution of the section of the jet due 

to the surface fall and 

m 



to the crest contraction 
is proportional to the 
length of the weir, the 
end contractions have 
nearly the same effect 
whether the weir is wide 
or narrow. 

J. B. Francis's experi- 
ments showed that a 
perfect end contraction, 
when the heads varied 
from 3 to 24 in., and 
the length of the weir 
was not less than three 
times the head, dimin- 
ished the effective 
length of the weir by 
an amount approxi- 
mately equal to one- 
tenth of the head. 
Hence, if I is the length 
of the notch or weir, and 
H the head measured 
behind the weir where 
the water is nearly still, 
then the width of the 
jet passing through the 
notch would be /—o-2H, 
allowing for two end 
contractions. In a weir 
divided by posts there 
may be more than two 
„ end contractions. 

45- Hence, generally, the 

width of the jet is I — o- iraH, where n is the number of end contractions 
of the stream. The contractions due to the fall of surface and to the 
crest contraction are proportional to the width of the jet. Hence, if cH 
is the thickness of the stream over the weir, measured at the contracted 
section, the section of the jet will be c(l— o-mH)H and (§ 41) the 
mean velocity will be f V(2gH). Consequently the discharge will 

be given by an equation of the form 

Q = fc(/-o-i«H)HV2gH 
= 5-35c(/-o-mH;Hi. 
This is Francis's formula, in which the coefficient of discharge c is 
much more nearly constant for different values of I and h than in 
the ordinary formula. Francis found for c the mean value 0-622, 
the weir being sharp-edged. 

§ 43. Triangular Notch (fig. 46). — Consider a lamina issuing be- 
tween the depths h and h+dh. Its area, neglecting contraction, will 
be bdh, and the velocity at that depth is V {2gh). Hence the dis- 
charge for this lamina is 

6V 2gh dh. 
But B/6 = H/(H-A);6 = B(H-«)/H. 

Hence discharge of lamina 

= B(H-/s)V (2gh)dh/H; 
and total discharge of notch rn 

= Q = BV(2g)Jo {H-h)Mdh/H 
= ABV(2g)H3. 




I or, introducing a coefficient to allow for contraction, 
Q = 1 VBV(2g)HJ, 
When a notch is used to gauge a stream of varying flow, the ratio 
B/H varies if the notch is rectangular, but is constant if the notch is 
triangular. This led Professor James Thomson to suspect that the 
coefficient of dis- 



charge, c, 
be much 
constant 
different 



would 
more 
with 

values 




Fig. 46. 



of H in a trian- 
gular than in a 
rectangular 
notch, and this 
has been experi- 
mentally shown 
to be the case. 
Hence a trian- 
gular notch is more suitable for accurate gaugings than a rectangular 
notch. For a sharp-edged triangular notcti Professor J. Thomson 
found c =0-617. It will be seen, as in § 41, that since JBH is the 
area of section of the stream through the notch, the formula is 
again of the form 

Q = cXiBHXW(2gH), 
where k = j% is the ratio of the mean velocity in the notch to the 
velocity at the depth H. it may easily be shown that for all notches 
the discharge can be expressed in this form. 

§ 44. Weir with a Broad Sloping Crest. — Suppose a weir formed 
with a broad crest so sloped that the streams flowing over it have a 
movement sensibly rectilinear and uniform (fig. 47). Let the inner 
ed^e be so rounded as to prevent a crest contraction. Consider a 
filament aa', the point a being so far back from the weir that the 




Fig. 47. 

velocity of approach is negligible. Let 00 be the surface level in the 
reservoir, and let a be at a height h" below OO, and h' above a'. 
Let h be the distance from OO to the weir crest and e the thickness 
of the stream upon it. Neglecting atmospheric pressure, which has 
no influence, the pressure at a is Gh" ; at a' it is Gz. If v be the 
velocity at a', 

&l2g = h' +h"-z = h - e ; 
Q = be V2g(fe— e). 
Theory does not furnish a value for e, but Q = o for e=o and for 
e = h. Q has therefore a maximum for a value of e between o and h, 
obtained by equating dQ/de to zero. This gives e = \h, and, inserting 

this value, 

0=0-385 bh^2gh, 
as a maximum value of the discharge with the conditions assigned. 
Experiment shows that the actual discharge is very approximately 
equal to this maximum, and the formula is more legitimately ap- 
plicable to the discharge over broad-crested weirs and to cases such 
as the discharge with free upper surface through large masonry 

Coefficients for the Discharge over Weirs, derived from the Experiments of T. E. Blackwell. When more than one experiment was made with the 
same head, and the results were pretty uniform, the resulting coefficients are marked with an (*). The effect of the converging wing-boards 
is very strongly marked. 



Headi in 

inches 
measured 


Sharp Edge. 


Planks 2 in. thick, square 


jn Crest. 


Crests 3 ft. wide. 












ro ft. long, 














from still 
Water in 


3 ft. long. 


10 ft. long. 


3 ft. long. 


6 ft. long. 


10 ft. long. 


wing-boards 
making an angle 


3 ft. long, 
level. 


3 ft. long, 
fall 1 in 18. 


3 ft. long, 
fall 1 in 12. 


6 ft. long, 
level. 


10 ft. long, 
level. 


10 ft. long, 
fall 1 in 18. 


Reservoir. 












of 6o°. 














I 


■677 


•809 


■467 


•459 


•435 l 


•754 


■452 


•545 


•467 




•381 


•467 


2 


•675 


•803 


■509* 


■561 


•585* 


•675 


•482 


•54° 


•533 




•479* 


•495* 


3 


•630 


•642* 


■563* 


•597* 


•569* 




•441 


•537 


•539 


•492* 






4 


•617 


•656 


•549 


•575 


•602* 


•656 


•419 


■43i 


•455 


•497* 




•515 


5 


•602 


•650* 


■588 


■601* 


•609* 


•671 


•479 


•516 






•518 




6 


•593 




■593* 


•608* 


■576* 




-501* 




■531 


•507 


•513 


•543 


7 






•617* 


•608* 


■576* 






•488 


•513 


■527 


•497 






8 




•581 


•606* 


•590* 


•548* 






•470 


•491 






•468 


•507 


9 




•530 


•600 


■569* 


•558* 






■476 


■492* 


•498 


•480* 


•486 




10 






•614* 


■539 


•534* 












•465* 


•455 




1 » 








•525 


•534* 












•467* 












•549* 








1 













'The discharge per second varied from -461 to -665 cub. ft. in two experiments. The coefficient -435 is derived from the mean value. 



DISCHARGE FROM ORIFICES] 



HYDRAULICS 



49 



sluice openings than the ordinary weir formula for sharp-edged 
weirs. It should be remembered, however, that the friction on 
the sides and crest of the weir has been neglected, and that this 
tends to reduce a little the discharge. The formula is equivalent 
to the ordinary weir formula with (-' = 0-577. 

Special Cases of Discharge from Orifices 

§ 45. Cases in which the Velocity of Approach needs to be taken 
into Account. Rectangular Orifices and Notches. — In finding the 
velocity at the orifice in the preceding investigations, it has been 
assumed that the head h has been measured from the free surface 
of still water above the orifice. In many cases which occur in 
practice the channel of approach to an orifice or notch is not so 
large, relatively to the stream through the orifice or notch, that the 
velocity in it can be disregarded. 

Let «i, hi (fig. 48) be the heads measured from the free surface to 
the top and bottom edges of a rectangular orifice, at a point in the 




Fig. 48. 

channel of approach where the velocity is u. It is obvious that a 
fall of the free surface, 

has been somewhere expended in producing the velocity u, and 
hence the true heads measured in still water would have been Ai + E) 
and A2 + 6. Consequently the discharge, allowing for the velocity 
of approach, is 

Q=I^VTg|(fe+h)i-(7; 1 +f|)5]. _ (1) 

And for a rectangular notch for which hi = o, the discharge is 

Q=icb^2g{(i h +i))i-m- _ (2) 

In cases where u can be directly determined, these formulae give the 
discharge quite simply. When, however, u is only known as a 
function of the section of the stream in the channel of approach, they 
become complicated. Let Q be the sectional area of the channel 
where h, and Ih are measured. Then «==Q/ U and fj = Q 2 /2g S2 2 . 

This value introduced in the equations above would render them 
excessively cumbrous. In cases therefore where U only is known, 
it is best to proceed by approximation. Calculate an approximate 
value Q' of Q by the equation 

Q.' = §c&V^I(M-fci*}. 
Then f) = Q' 2 /2g!2 2 nearly. This value of 6 introduced in the equations 
above will give a second and much more approximate value of Q. 

§ 46. Partially Submerged Rectangular Orifices and Notches. — 
When the tail water is above the lower but below the upper edge 
of the orifice, the flow in the two parts of the orifice, into which it 
is divided by the surface of the tail water, takes place under different 
conditions. A filament MjOTi (fig. 49) in the upper part of the 
orifice issues with a head h' which may have any value between 




Qi = fc&V2g{fci-M) ) 
Qz = cb(h 2 -h)^2gh f 



(3) 

In the case of a rectangular notch or weir, hi = o. Inserting this 
value, and adding the two portions of the discharge together, we get 
for a drowned weir 

Q = cb^Tgh(,h 2 -h/ 2 ), (4) 

where h is the difference of level of the head and tail water, and fc 
is the head from the free surface above the weir to the weir crest 
(fig. 50). 

From some experiments by Messrs A. Fteley and F. P. Stearns 
(Trans. Am. Soc. C.E., 1883, p. 102) some values of the coefficient c 
can be reduced 



Fig. 49. 

hi and h. But a filament M 2 m 2 issuing in the lower part of the 
orifice has a velocity due to h" — h"', or k, simply. In the upper part 
of the orifice the head is variable, in the lower constant. If Qi, Q2 
are the discharges from the upper and lower parts of the orifice, 
b the width of the orifice, then 



ha/fa 


c" 


h/h 2 


c 


O-I 


0-629 


0-7 


0-578 


0-2 


0-614 


o-8 


0-583 


o-3 


o-6oo 


0-9 


0-596 


0-4 


0-590 


o-95 


0-607 


o-5 


0-582 


I -00 


0-628 


06 


0-578 








If velocity of approach is taken into account, let \ be the head due 
to that velocity ; then, adding 6 to each of the heads in the equations 
(3), and reducing, we get for a weir 

Q=cbT]Tg[(h 2 +i))(h+W-i(h+W-im; (5) 

an equation which may be useful in estimating flood discharges. 

Bridge Piers and other Obstructions in Streams. — When the piers 
of a bridge are erected in a stream they create an obstruction to the 
flow of the stream, which 
causes a difference of surface- 
level above and below the 
pier (fig. 51). If it is neces- 
sary to estimate this differ- 
ence of level, the flow 
between the piers may be 
treated as if it occurred over 
a drowned weir. But the 

value of c in this case is 'v/////yy/yy/yy;s^yyjyj;syZ4My/Jss!;Jsyji,>.' ■ -• 
imperfectly known. Fig. 50. 

§ 47. Bazin's Researches on 
Weirs. — H. Bazin has executed a long series of researches on the 
flow over weirs, so systematic and complete that they almost 
supersede other observations. The account of them is contained 
in a series of papers in the Annates des Ponts et Chaussees 
(October 1888, January 1890, November 1891, February 1894, 
December 1896, 2nd trimestre 1898). Only a very abbreviated 
account can be given here. The general plan of the experiments 
was to establish first the coefficients of discharge for a standard 
weir without end contractions; next to establish weirs of other 
types in series with the standard weir on a channel with steady 
flow, to compare the observed heads on the different weirs and 
to determine their coefficients from the discharge computed at 
the standard weir. A channel was constructed parallel to the 
Canal de Bourgogne, taking water from it through three sluices 
0-3X1-0 metres. The water enters a masonry chamber 15 metres 
long by 4 metres wide where it is stilled and passes into the canal 
at the end of which is the standard weir. The canal has a length 
of 15 metres, a width of 2 metres and a depth of 1-6 metres. From 




mmmmmmmmM. 
Fig. 51.1 

this extends a channel 200 metres in length with a slope of 1 mm. 
per metre. The channel is 2 metres wide with vertical sides. The 
channels were constructed of concrete rendered with cement. The 
water levels were taken in chambers constructed near the canal, 
by floats actuating an index on a dial. Hook gauges were used in 
determining the heads on the weirs. 

Standard Weir. — The weir crest was 3-72 ft. above the bottom 
of the canal and formed by a plate i in. thick. It was sharp-edged 
with free overfall. It was as wide as the canal so that end con- 
tractions were suppressed, and enlargements were formed below 
the crest to admit air under the water sheet. The channel below 
the weir was used as a gauging tank. Gaugings were made with the 
weir 2 metres in length and afterwards with the weir reduced to 
1 metre and 0-5 metre in length, the end contractions being sup- 
pressed in all cases. Assuming the general formula 

Q = mlH{2gh), (1) 



5o 

Bazin arrives at the following values of m : — 

Coefficients of Discharge of Standard Weir. 



HYDRAULICS 



[DISCHARGE FROM ORIFICES 



Head h metres. 


Head h feet. 


m 


0-05 


•164 


0-4485 I 


O-IO 


■328 


0-4336 ! 


0-15 


•492 


0-4284 ! 


0-20 


•656 


0-4262 


0-25 


•820 


o-4259 1 


0-30 


•984 


0-4266 j 


o-35 


1-148 


o-4275 j 


0-40 


1-312 


0-4286 


o-45 


1-476 


0-4299 


0-50 


1-640 


o-43i3 


o-55 


1-804 


0-4327 


o-6o 


1-968 


0-4341 



Bazin compares his results with those of Fteley and Stearns in 1877 
and 1879, correcting for a different velocity of approach, and finds 
a close agreement. 

Influence of Velocity of Approach. — To take account of the velocity 
of approach u it is usual to replace h in the formula by h+ay?/2g 
where o is a coefficient not very well ascertained. Then 
Q = M /(fc+a«*/2g)V \2g{h + au'/2g)} 

=nlhT](2gh){i+aii i !2gh)i. (2) 

The original simple equation can be used if 
m = )i(l-\-au 2 l2gh)i 
or very approximately, since u?J2gh is small, 

m=n{i+Uu'l2gh). (3) 

Now if p is the height of the weir crest above the bottom of the 

canal (fig. 52), « = Q//(/>+ft). 
Replacing Q by its value 
in (1) 

= m?{h((,p+h)\\ (4) 
so that (3) may be written 

m=*[i+k{h[(p+h)n. (5) 
Gaugings were made with 
weirs of 0-75, 0-50, 0-35, and 
0-24 metres height above 
the canal bottom and the 
results compared with those of the standard weir taken at the same 
time. The discussion of the results leads to the following values of 
m in the general equation (1) : — 

W=M(l+2-5M 2 /2gW 

=n[i+o-55\h/(.P+h)n. 
Values of m — 




w//////////////////////mc 

Fig. 52. 



Head h metres. 


Head h feet. 





0-05 . 


•164 


0-4481 


O-IO 


•328 


0-4322 


0-20 


■656 


p-4215 


0-30 


.984 


0-4174 


0-40 


1-312 


0-4144 


0-50 


1-640 


0-4118 


o-6o 


1-968 


0-4092 



An approximate formula for y. is : 

M = 0-405 +0-003//! (h in metres) 

M = 0-405+0-01 (h (h in feet). 
Inclined Weirs.- — Experiments were made in which the plank weir 
was inclined up or down stream, the crest being sharp and the end 
contraction suppressed. The following are coefficients by which 
the discharge of a vertical weir should be multiplied to obtain the 
discharge of the inclined weir. 



Inclination up stream 



Vertical weir 
Inclination down stream 



1 to 1 
3 to 2 
3 to 1 



Coefficient. 

o-93 
0-94 
0-96 
1 -oo 
1-04 
1-07 

I-IO 
I-I2 
1-09 



from the weir, but encloses a volume of air which is at less than 
atmospheric pressure, and the tail water rises under the sheet. 
The discharge is a little greater than for free overfall. At greater 
head the air disappears from below the sheet and the sheet is said 
to be " drowned." The drowned sheet may be independent of the 
tail water level or influenced by it. In the former case the fall is 
followed by a rapid, terminating in a standing wave. In the latter 

case when the foot of the _ _ _ _ 

sheet is drowned the level - - - - - -T— ^o^^ 

of the tail water influences b Vc- 

the discharge even if it is 
below the weir crest. 

Weirs with Flat Crests.— 
The water sheet may spring 

clear from the upstream edge . 

or may adhere to the fa%V/jMW/////////////, 



m 



■ 3 to I 
,, „ 3 to 2 

1 to 1 

,, I to 2 

1 to 4 

The coefficient varies appreciably, if h/p approaches unity, which 
case should be avoided. 

In all the preceding cases the sheet passing over the weir is de- 
tached completely from the weir and its under-surface is subject 
to atmospheric pressure. These conditions permit the most exact 
determination of the coefficient of discharge. If the sides of the 
canal below the weir are not so arranged as to permit the access 
of air under the sheet, the phenomena are more complicated. So 
long as the head does not exceed a certain limit the sheet is detached 




W////S////////J 



crest falling free beyond the 
downstream edge. In the 
former case the condition is that of a sharp-edged weir and it is 
realized when the head is at least double the width of crest. It may 
arise if the head is at least i^ the width of crest. Between these 
limits the condition of the sheet is unstable. When the sheet 
is adherent the coefficient m depends on the ratio of the head h 
to the width of crest c (fig. 53), and is given by the equation 
m = mi [0-70+0- i85h/c], where mi is the coefficient for a sharp- 
edged weir in similar con- 
ditions. Rounding the up- 
stream edge even to a small 
extent modifies the dis- 
charge. If R is the radius 
of the rounding the co- 
efficient m is increased in 
the ratio 1 to 1 +R/& nearly. 
The results are limited to R 
less than \ in. 

Drowned Weirs.— Let h ^^^p^^W5^?W^ 
(fig. 54) be the height of F 

head water and hi that of . . 

tail water above the weir crest. Then Bazin obtains as the approxi- 
mate formula for the coefficient of discharge 

m = 1 -05Wi[i +lhlp] $ { Qi - hi)lh), 
where as before mi is the coefficient for a sharp-edged weir in similar 
conditions, that is, 
when the sheet is 
free and the weir 
of the same height. 
§ 48. Separating 
Weirs. — Many 
towns derive their 
water-supply from 
streams in high 
m o o rl a n d dis- 
tricts, in which the 
flow is extremely variable. The water is collected in large storage 
reservoirs, from which an uniform supply can be sent to the town. In 





Fig. 55. 



JPlarv of 

C&st Iran 

Key 




Fig. 56. 

such cases it is desirable to separate the coloured water which comes 
down the streams in high floods from the purer water of ordinary 
flow. The latter is sent into the reservoirs; the former is allowed 



DISCHARGE FROM ORIFICES] 



HYDRAULICS 



5 1 



to flow away down the original stream channel, or is stored in 
separate reservoirs and used as compensation water. To accomplish 
the separation of the flood and ordinary water, advantage is taken of 
the different horizontal range of the parabolic path of the water 
falling over a weir, as the depth on the weir and, consequently, the 
velocity change. Fig. 55 shows one of these separating weirs in the 
form in which they were first introduced on the Manchester Water- 
works; fig. 56 a more modern weir of the same kind designed by 
Sir A. Binnie for the Bradford Waterworks. When the quantity of 
water coming down the stream is not excessive, it drops over the 
weir into a transverse channel leading to the reservoirs. In flood, 
the water springs over the mouth of this channel and is led into a 
waste channel. 

' It may be assumed, probably with accuracy enough for practical 
purposes, that the particles describe the parabolas due to the mean 
velocity of the water passing over the weir, that is, to a velocity 

§V(2gfc), 

where h is the head above the crest of the weir. 

Let cb = x be the width of the orifice and ac=y the difference of 
level of its edges (fig. 57). Then, if a particle passes from a to b in t 
seconds, 

y = \gf, * = f V(2gfc)<; 

■ :y=&xi/h, 

which gives the width * for any given difference of level y and head 

h, which the jet will just pass over the orifice. Set off ad vertically 




9 

2 



^ \\\ :-■•'' ; 

\^\ W:\; ;- ■ 

\N\VJH i 

V\\\KI ■-•: 

\\\ :\: 



O 1 



\ V, 



d 



A e 



-i-^h- 



Fig. 57. 

and equal to §g on any scale; af horizontally and equal to | V (g^)- 
Divide af, fe into an equal number of equal parts. Join a with the 
divisions on ef. The intersections of these lines with verticals from 
the divisions on af give the parabolic path of the jet. 

Mouthpieces — Head Constant 

§ 49. Cylindrical Mouthpieces. — When water issues from, a short 
cylindrical pipe or mouthpiece of a length at least equal to I J times 
its smallest transverse dimension, the stream, after contraction within 
the mouthpiece, expands to fill it and issues full bore, or without 
contraction, at the point of discharge. The discharge is found to 
be about one-third greater than that from a simple orifice of the 
same size. On the other hand, the energy of the fluid per unit of 
weight is less than that of the stream from a simple orifice with the 
same head, because part of the energy is wasted in eddies produced 
at the point where the stream expands to fill the mouthpiece, the 
action being something like that which occurs at an abrupt change 
of section. 

Let fig. 58 represent a vessel discharging through a cylindrical 
mouthpiece at the depth h from the free surface, and let the axis of 
the jet XX be taken as the datum with reference to which the head 
is estimated. Let 12 be the area of the mouthpiece, o> the aiea of 
the stream at the contracted section EF. Let v, p be the velocity 
and pressure at EF, and vi, p\ the same quantities at GH. If the 
discharge is into the air, pi is equal to the atmospheric pressure p a . 

The total head of any filament which goes to form the jet, taken 



at a point where its velocity is sensibly zero, is h-\-p a jG; at EF the 
total head is v^feg+p/G; at GH it is vf^g+pi/G. 

Between EF and GH there is a loss of head due to abtupt change 
of velocity, which from eq. (3), § 36, may have the value 

(»-Z>l) 2 /2g. 

Adding this head lost to the head at GH, before equating it to the 
heads at EF and at the point where the filaments start into motion, — 

h+pa/G =vy 2 g+p/G = Vl *l2g+p i IG+{v-v l yi2g. 
But arj = Qvi, and w=c c ft, if c c is the coefficient of contraction within 
the mouthpiece. Hence 

» = fii'i/o^ri/c. 
Supposing the discharge into the air, so that pi=p«, 

h+p„IG=v^f 2 g+p a /G-\-(v l V2g) (l/c-i)*; 
(»i/?f) (i+(ifc-i) 2 j=A; 
••■ vi= ,1 (2gh)H [i + U/cc-i)*); (1) 

where the coefficient on the right is evidently the coefficient of velocity 
for the cylindrical 
mouthpiece in terms of 
the coefficient of con- 
traction at EF. Let 
£0=0-64, the value for 
simple orifices, then the 
coefficient of velocity is 

c„ = i/V!i+(i/cc-i) ! ! 
=0-87 (2) 

The actual value of c v 
found by experiment is 
0-82, which does not 
differ more from the 
theoretical value than 
might be expected if 
the friction of the 
mouthpiece is allowed 
for. 
GH, 

C„=0-82 




Fig. 58. 
Hence, for mouthpieces of this kind, and for the section at 



c c = i-oo c = o-82, 

Q=0-82flV(2g/t). 

It is easy to see from the equations that the pressure p at EF is 
less than atmospheric pressure. Eliminating v u we get 

(pa~P)IG = ih nearly; (3) 

or P = P*~ iGhVo per sq. ft. 

If a pipe connected with a reservoir on a lower level is introduced 
into the mouthpiece at the part where the contraction is formed 
(fig- 59)i the water will rise in this pipe to a height 

KL = (/>„-£)/G = ffc nearly. 
If the distance X is less than this, the water from the lower reservoir 
will be forced continuously into the jet by the atmospheric pressure, 
and discharged with it. This is the crudest form of a kind of pump 
known as the jet pump. 

§ 50. Convergent Mouthpieces. — With convergent mouthpieces 
there is a contraction within the mouthpiece causing a loss of head, 
and a diminution of the velocity of discharge, as with cylindrical 
mouthpieces. There is also a second contraction of the stream out- 
side the mouthpiece. Hence the discharge is given by an equation 
of the form 

Q=Cc c QV(2gft), _ (4) 

where fl is the area of the external end of the mouthpiece, and c c Sl 
the section of the contracted jet beyond the mouthpiece. 

Convergent Mouthpieces (Castel's Experiments). — Smallest diameter of 
orifice = 0-05085 //. Length of mouthpiece — 2-6 Diameters. 



Angle of 
Convergence. 


Coefficient of 


Coefficient of 


Coefficient of 


Contraction, 

Cc 


Velocity, 

Cv 


Discharge, 
c 


0° 0' 


•999 


•830 


•829 


i°3°' 


i- 000 


■866 




866 


3° 10' 


I-OOI 


•894 




895 


4° 10' 


1-002 


•910 




912 


K 26 ', 


I-004 


■920 




924 


7° 52' 


•998 


•931 




929 


8° 58' 


•992 


•942 




934 


10° 20' 


•987 


•950 




938 


12° 4' 


•986 


•955 




942 , 


13° 24' 


•983 


•962 




946 


14 28 


•979 


•966 




941 


16° 36' 


.969 


•971 




938 


19" 28' 


•953 


•97° 




924 


21° O' 


•945 


•971 




918 


23° 0' 


•937 


•974 




913 


29° 58' 


•919 


•975 




896 


40 20 


•887 


•980 




869 


4 8° 50' 


•861 


■984 


•847 



The maximum coefficient of discharge is that for a mouthpiece 
with a convergence of 13 24'. 



HYDRAULICS 





The values of c v and c c must here be determined by experiment. 
The above table gives values sufficient for practical purposes. Since 

the contraction beyond 
the mouthpiece increases 
with the convergence, or, 
what is the same thing, 
c c diminishes, and on the 
other hand the loss of 
energy diminishes, so 
that Cv increases with 
the convergence, there 
is an angle for which the 
product c c c v , and con- 
sequently the discharge, 
•is a maximum. 

§ 51. Divergent Con- 
oidal Mouthpiece. — Sup- 
pose a mouthpiece so 
designed that there is 
no abrupt change in the 
section or velocity of 
the stream passing 
through it. It may 
have a form at the 
inner end approxi- 
mately the same as 
that of a simple contracted vein, and may then enlarge gradu- 
ally, as shown in fig. 60. Suppose that at EF it becomes 
cylindrical, so that the jet may be taken to be of the diameter 
EF. Let <j, v, p be the section, velocity and pressure at CD, 
and Q, v u pi the same quantities at EF, p a being as usual the 
atmospheric pressure, or pressure on the free surface AB. Then, 

since there is no loss of 
energy, except the small 
frictional resistance of the 
surface of the mouthpiece, 
h+p a /G=vy 2 g+p/G 

=y/2g+£./G. 

If the jet discharges into 
the air, pi=pa) and 
Vi 2 l2g = h; 
v, = V (2gh) ;_ 
or, if a coefficient is intro- 
duced to allow for friction, 

»i = c_v V (2gh) ; 
where c v is about 0-97 if 
the mouthpiece is smooth 
and well formed. 

Q = Qoi=c»nV (2gh). 
Hence the discharge de- 
pends on the area of the 
stream at EF, and not at 
all on that at CD, and the 
latter may be made as 
small as we please without 
affecting the amount of 
water discharged. 
There is, however, a limit to this. .As the velocity at CD is greater 
than at EF the pressure is less, and therefore less than atmospheric 
pressure, if the discharge is into the air. If CD is so contracted that 
p=o, the continuity of flow is impossible. In fact the stream 

disengages itself from the 
mouthpiece for some value 
of p greater than o (fig. 61). 
From the equations, 

plG=PajG-{v>-v?)l2g. 
Let Uja=m. Then 

v — v\m ; 
£/G = />«/G-f, ! (»» 2 -i)/2g 
= Pa/G-(m 2 -i)h; 

whence we find that pjG 
will become zero or nega- 
tive if 

ahm^J\(h+pJG)lh\ 
-V!i+A./GA); 

or, putting £«/G = 34 ft., if 

In practice there will be an interruption of the full bore flow with 
a less ratio of Sljw, because of the disengagement of air from the water. 
But, supposing this does not occur, the maximum discharge of a 
mouthpiece of this kind is 

Q= w V{2g(A+*>./G)|; 
that is, the discharge is the same as for a well-bellmouthed mouth- 
piece of area a, and without the expanding part, discharging into 
a vacuum. 

§ 32. Jet Pump. — A divergent mouthpiece may be arranged to act 
as a pump, as shown in fig. 62. The water which supplies the energy 



[DISCHARGE OF ORIFICES 



Fig. 60. 




required for pumping enters at A. The water to be pumped enters 
at B. The streams combine at DD where the velocity is greatest 
and the pressure least. Beyond DD the stream enlarges in section, 




Fig. 62. 

arid its pressure increases, till it is sufficient to balance the head due 
to the height of the lift, and the water flows away by the discharge 
pipe C. 

Fig. 63 shows the whole arrangement in a diagrammatic way. 
A is the reservoir which supplies the water that effects the pumping; 




Fig. 63. 

B is the reservoir of water to be pumped ; C is the reservoir into 
which the water is pumped. 

Discharge with Varying Head 

§ 53. Flow from a Vessel when the Effective Head varies with the 
Time. — Various useful problems arise relating to the time of empty- 
ing and filling vessels, reservoirs, lock chambers, &c, where the flow 
is dependent on a head which increases or diminishes during the 
operation. The simplest of these problems is the case of filling or 
emptying a vessel of constant horizontal section. 

Time of Emptying or Filling a Vertical-sided Lock Chamber. — 
Suppose the lock chamber, which has a water surface of O square 
ft., is emptied through a sluice in the tail gates, of area w, placed 
below the tail-water level. Then the effective head producing flow 
through the sluice is the difference of level in the chamber and tail 
bay. Let H (fig. 64) be the initial difference of level, h the difference 



Head, water Uvr.l 




Fig. 64. 

of level after t seconds. Let — dh be the fall of level in the chamber 
during an interval dt. Then in the time dt the volume in the chamber 
is altered by the amount —Qdh, and the outflow from the sluice in 
the same time is cuV {2gh)dt. Hence the differential equation con- 
necting h and t is 

cwV (2gh)dt+Qh =0. 



DISCHARGE FROM ORIFICES] 



HYDRAULICS 



53 



For the time /, during which the initial head H diminishes to any 
other value h, 



-in/(<W2g)j f dhHh= C'dt. 



.•.t = 2Q(VH-VA)/{c«V(2g)} 
= (Q/c«)(V(2H/g)-V(2A/g)}. 
For the whole time of emptying, during which h diminishes from 
H to o, 

T = (Q/c w )V(2H/g). 
Comparing this with the equation for flow under a constant head, 
it will be seen that the time is double that required for the discharge 
of an equal volume under a constant head. 

The time of filling the lock through a sluice in the head gates is 
exactly the same, if the sluice is below the tail-water level. But if 
the sluice is above the tail-water level, then the head is constant 
till the level of the sluice is reached, and afterwards it diminishes 
with the time. 

Practical Use of Orifices in Gauging Water 
§ 54. If the water to be measured is passed through a known orifice 
under an arrangement by which the constancy of the head is ensured, 
the amount which passes in a given time can be ascertained by the 
formulae already given. It will obviously be best to make the 
orifices of the forms for which the coefficients are most accurately 
determined; hence sharp-edged orifices or notches are most com- 
monly used. 

Water Inch. — For measuring small quantities of water circular 
sharp-edged orifices have been used. The discharge from a circular 
orifice one French inch in diameter, with a head of one line above the 
top edge, was termed by the older hydraulic writers a water-inch. 
A common estimate of its value was 14 pints per minute, or 677 
English cub. ft. in 24 hours. An experiment by C. Bossut gave 
634 cub. ft. in 24 hours (see Navier's edition of Belidor's Arch. 
Hydr., p. 212). 

L. J. Weisbach points out that measurements of this kind would be 
made more accurately with a greater head over the orifice, and he 
proposes that the head should be equal to the diameter of the orifice. 
Several equal orifices may be used for larger discharges. 

Pin Ferrules or Measuring Cocks. — To give a tolerably definite 
supply of water to houses, without the expense of a meter, a ferrule 
with an orifice of a definite size, or a cock, is introduced in the 
service-pipe. If the head in the water main is constant, then a 
definite quantity of water would be delivered in a given time. The 
arrangement is not a very satisfactory one, and acts chiefly as a 
check on extravagant use of water. It is interesting here chiefly as 
an example of regulation of discharge by means of an orifice. Fig. 65 

shows a cock of 
this kind used at 
Zurich. It consists 
of three cocks, the 
middle one having 
the orifice of the 
predetermined size 
in a small circular 
plate, protected by 
wire gauze from 
stoppage by im- 
purities in the 
water. The cock 
p IG g, on the right hand 

can be used by the 
consumer for emptying the pipes. The one on the left and the 
measuring cock are connected by a key which can be locked by a 
padlock, which is under the control of the water company. 

§ 55. Measurement of the Flow in Streams. — To determine the 
quantity of water flowing off the ground in small streams, which is 
available for water supply or for obtaining water power, small 
temporary weirs are often used. These may be formed of planks 
supported by piles and puddled to prevent leakage. The measure- 
ment of the head may be made by a thin-edged scale at a short 
distance behind the weir, where the water surface has not begun to 
slope down to the weir and where the velocity of approach is not 
high. The measurements are conveniently made from a short pile 
driven into the bed of the river, accurately level with the crest of 
the weir (fig. 66). Then if at any moment the head is h, the dis- 
charge is, for a rectangular notch of breadth b, 

Q = §c«*V2l¥ 
where c = o-62; or, better, the formula in § 42 may be used. 

Gauging weirs are most commonly in the form of rectangular 
notches; and care should be taken that the crest is accurately 
horizontal, and that the weir is normal to the direction of flow of 
the stream. If the planks are thick, they should be bevelled (fig. 67), 
and then the edge may be protected by a metal plate about ^th 
in. thick to secure the requisite accuracy of form and sharpness of 
edge. In permanent gauging weirs, a cast steel plate is sometimes 
used to form the edge of the weir crest. The weir should be large 
enough to discharge the maximum volume flowing in the stream, 
and at the same time it is desirable that the minimum head should 




not be too small (say half a foot) to decrease the effects of errors of 
measurement. The section of the jet over the weir should not exceed 
one-fifth the section of the stream behind the weir, or the velocity 
of approach will need to be taken into account. A triangular notch 
is very suitable for measurements of this kind. 

If the flow is variable, the head h must be recorded at equidistant 
intervals of time, say twice daily, and then for each 12-hour period 



Seal 



Weir 





Fig. 66. 

the discharge must be calculated for the mean of the heads at the 
beginning and end of the time. As this involves a good deal of 
troublesome calculation, E. Sang proposed to use a scale so graduated 
as to read off the discharge in cubic feet per second. The lengths of 
the principal graduations of such a scale are easily calculated by 
putting Q = l,2, 3 . . . in the ordinary formulae for notches; 
the intermediate graduations may be taken accurately enough by 
subdividing equally the distances between the principal graduations. 

The accurate measurement of the discharge of a stream by means 
of a weir is, however, in practice, rather more difficult than might 
be inferred from 
the simplicity of 
the principle of the 
operation. Apart 
from the difficulty 
of selecting a suit- 
able coefficient of 
discharge, which 
need not be serious 
if the form of the 
weir and the nature 
of its crest are pro- 
perly attended to, t? t _ ^ 
other difficulties of * IG " ° 7 ' 
measurement arise. The length of the 
weir should be very accurately deter- 
mined, and if the weir is rectangular 
its deviations from exactness of level 
should be tested. Then the agitation 
of the water, the ripple on its surface, 
and the adhesion of the water to the 
scale on which the head is measured, 
are liable to introduce errors. Upon a 
weir 10 ft. long, with I ft. depth of 
water flowing over, an error of l-ioooth 
of a foot in measuring the head, or an 
error of i-iooth of a foot in measuring 
the length of the weir, would cause an 
error in computing the discharge of 
2 cub. ft. per minute. 

Hook Gauge. — For the determination 
of the surface level of water, the most 
accurate instrument is the hook gauge 
used first by U. Boyden of Boston, in 
1840. It consists of a fixed frame with 
scale and vernier. In the instrument 
in fig. 68 the vernier is fixed to the 
frame, and the scale slides vertically. 
The scale carries at its lower end a hook 
with a fine point, and the scale can be 
raised or lowered by a fine pitched 
screw. If the hook is depressed below 

the water surface and then raised by the screw, the moment of its 
reaching the water surface will be very distinctly marked, by the 
reflection from a small capillary elevation of the water surface over 
the point of the hook. In ordinary light, differences of level of the 
water of -ooi of a foot are easily detected by the hook gauge. If such 
a gauge is used to determine the heads at a weir, the hook should 



==liE=? 



Fig. 68 



54 



HYDRAULICS 



[DISCHARGE FROM ORIFICES 



first be set accurately level with the weir crest, and a reading taken. 
Then the difference of the reading at the water surface and that 
tor the weir crest will be the head at the weir. 

§ 56. Modules used in Irrigation. — In distributing water for 
irrigation, the charge for the water may be simply assessed on the 
area of the land irrigated for each consumer, a method followed in 
India; or a regulated quantity of water may be given to each 
consumer, and the charge may be made proportional to the quantity 
of water supplied, a method employed for a long time in Italy and 
other parts of Europe. To deliver a regulated quantity of water 




time to time. It has further the advantage that the cultivator, by 
observing the level of the water in the chamber, can always see 
whether or not he is receiving the proper quantity of water. 

On each canal the orifices are of the same height, and intended to 
work with the same normal head, the width of the orifices being 
varied to suit the demand for water. The unit of discharge varies on 
different canals, being fixed in each case by legal arrangements. 
Thus on the Canal Lodi the unit of discharge or one module of water 
is the discharge through an orifice 1-12 ft. high, 0-12416 ft. wide, 
with a head of 0-32 ft. above the top edge of the orifice, or -88 ft. 
above the centre. This corresponds to a discharge of about 0-6165 
cub. ft. per second. 

In the most elaborate Italian modules the regulating chamber is 
arched over, and its dimensions are very exactly prescribed. Thus 
in the modules of the Naviglio Grande of Milan, shown in fig. 70, 
the measuring orifice is cut in a thin stone slab, and so placed that 
the discharge is into the air with free contraction on all sides. The 






Fig. 69. 

from the irrigation channel, arrangements termed modules are used. 
These are constructions intended to maintain a constant or approxi- 
mately constant head above an orifice of fixed size, or to regulate 
the size of the orifice so as to give a constant discharge, notwith- 
standing the variation of level in the irrigating channel. 

§ 57. Italian Module. — The Italian modules are masonry construc- 
tions, consisting of a regulating chamber, to which water is admitted 
by an adjustable sluice from the canal. At the other end of the 
chamber is an orifice in a thin flagstone of fixed size. By means 
of the adjustable sluice a tolerably constant head above the fixed 
orifice is maintained, and therefore there is a nearly constant dis- 
charge of ascertainable amount through the orifice, into the channel 
leading to the fields which are to be irrigated. 

In fig. 69, A is the adjustable sluice by which water is admitted 
to the regulating chamber, B is the fixed orifice through which the 
water is discharged. The sluice A is adjusted from time to time by 
the canal officers, so as to bring the level of the water in the regulating 
chamber to a fixed level marked on the wall of the chamber. When 





r adjusted it is locked. Let ui be the area of the 
orifice through the sluice at A, and u 2 that of the 
fixed orifice at B ; let hi be the difference of level 
between the surface of the water in the canal and 
regulating chamber; h« the head above the centre of 
the discharging orifice, when the sluice has been 
adjusted and the flow has become steady; Q the 
normal discharge in cubic feet per second. Then, 
since the flow through the orifices at A and B is the same, 

Q = ciwi V (2gh) = C2U2V (2gh) , 

where c\ and c 2 are the coefficients of discharge suitable for the two 
orifices. Hence 

Cimi/c2«2 = V (hilhi). 

If the orifice at B opened directly into the canal without any 
intermediate regulating chamber, the discharge would increase for 
a given change of level in the canal in exactly the same ratio. Conse- 
quently the Italian module in no way moderates the fluctuations of 
discharge, except so far as it affords means of easy adjustment from 



Fig. 71. 

adjusting sluice is placed with its sill flush with the bottom of the 
canal, and is provided with a rack and lever and locking arrange- 
ment. The covered regulating chamber is about 20 ft. long, with 
a breadth 1-64 ft. greater than that of the discharging orifice. At 
precisely the normal level of the water in the regulating chamber, 
there is a ceiling of planks intended to still the agitation of the 
water. A block of stone serves to indicate the normal level of 
the water in the chamber. The water is discharged into an open 
channel 0-655 ft- wider than the orifice, splaying out till it is 1-637 
ft. wider than the orifice, and about 18 ft. in length. 

§ 58. Spanish Module. — On the canal of Isabella II., which supplies 
water to Madrid, a module much more perfect in principle than the 
Italian module is employed. Part of the water is supplied for irriga- 
tion, and as it is very valuable its 
strict measurement is essential. The 
module (fig. 72) consists of two 
chambers one above the other, the 
upper chamber being in free communi- 
cation with the irrigation canal, and 
the lower chamber discharging by a 
culvert to the fields. In the arched 
roof between the chambers there is a 
circular sharp-edged orifice in a bronze 
plate. Hanging in this there is a 
bronze plug of variable diameter sus- 
pended from a hollow brass float. If 
the water level in the canal lowers, the 
plug descends and gives an enlarged 
opening, and conversely. Thus a per- 
fectly constant discharge with a vary- 
ing head can be obtained, provided no 
clogging or silting of the chambers pre- 
vents the free discharge of the water 
or the rise and fall of the float. The theory of the module is very 
simple. Let R (fig. 71) be the radius of the fixed opening, r the 
radius of the plug at a distance h from the plane of flotation of the 
float, and Q the required discharge of the module. Then 

Taking c =0-63, 

Q = i5-88(R 2 -r ! )Vfe; 
r = V!R 2 -Q/i5-88V^|. 

Choosing a value for R, successive values of r can be found for 
different values of h, and from these the curve of the plug can be 
drawn. The module shown in fig. 72 will discharge I cubic metre per 
second. The fixed opening is 0-2 metre diameter, and the greatest 
head above the fixed orifice is I metre. The use of this module 
involves a great sacrifice of level between the canal and the fields. 
The module is described in Sir C. Scott-Moncrieff ' s Irrigation in 
Southern Europe. 

§ 59. Reservoir Gauging Basins. — In obtaining the power to store 
the water of streams in reservoirs, it is usual to concede to riparian 



DISCHARGE FROM ORIFICES] 



HYDRAULICS 



55 



owners below the reservoirs a right to a regulated supply through- 
out the year. This compensation water requires to be measured in 
such a way that the millowners and others interested in the matter 
can assure themselves that they are receiving a proper quantity, and 
they are generally allowed a certain amount of control as to the 
times during which the daily supply is discharged into the stream. 




Fig. 74 shows an arrangement designed for the Manchester water 
works. The water enters from the reservoir a chamber A, the object 
of which is to still the irregular motion of the water. The admission 
is regulated by sluices at b, b, b. The water is discharged by orifices 
or notches at a, a, over which a tolerably constant head is maintained 
by adjusting the sluices at b, b, b. At any time the millowners can 
see w'hether the discharge is given and whether the proper head is 
maintained over the orifices. To test at any time the discharge of 
the orifices, a gauging basin B is provided. The water ordinarily 



flows oyer this, without entering it, on a floor of cast-iron plates. 
If the discharge is to be tested, the water is turned for a definite time 
into the gauging basin, by suddenly opening and closing a sluice at c. 
The volume of flow can be ascertained from the depth in the gauging 
chamber. A mechanical arrangement (fig. 73) was designed for 
securing an absolutely constant head over the orifices at a, a. The 
orifices were formed in a cast-iron plate capable of sliding up and 




Fig. 73. — Scale T | . 

down, without sensible leakage, on the face of the wall of the chamber. 
The orifice plate was attached by a link to a lever, one end of which 
rested on the wall and the other on floats / in the chamber A. The 
floats rose and fell with the changes of level in the chamber, and 
raised and lowered the orifice plate at the same time. This 




Fig. 74.— Scale 5 J B . 

mechanical arrangement was not finally adopted, careful watching 
of the sluices at b, b, b, being sufficient to secure a regular discharge. 
The arrangement is then equivalent to an Italian module, but on a 
large scale. 

§ 60. Professor Fleeming Jenkin's Constant Flow Valve. — In the 
modules thus far described constant discharge is obtained by vary- 
ing the area of the orifice through which the water flows. Professor 
F. Jenkin has contrived a valve in which a constant pressure head 
is obtained, so that the orifice need not be varied {Roy. Scot. Society 



56 



HYDRAULICS 



[COMPRESSIBLE FLUIDS 



of Arts, 1876). Fig. 75 shows a valve of this kind suitable for a 
6-in. water main. The water arriving by the main C passes through 
an equilibrium valve D into the chamber A, and thence through a 
sluice 0, which can be set for any required area of opening, into the 
discharging main B. The object of the arrangement is to secure a 
constant difference of pressure between the chambers A and B, so 
that a constant discharge flows through the stop valve O. The 
equilibrium valve D is rigidly connected with a plunger P loosely 
fitted in a diaphragm, separating A from a chamber B2 connected by 
a pipe Bi with the discharging main B. Any increase of the differ- 
ence of pressure in A and B will drive the plunger up and close the 




Fig. 75. — Scale 4 4 . 

equilibrium valve, and conversely a decrease of the difference of 
pressure will cause the descent of the plunger and open the equilibrium 
valve wider. Thus a constant difference of pressure is obtained in 
the chambers A and B. Let w be the area of the plunger in square 
feet, p the difference of pressure in the chambers A and B in pounds 
per square foot, w the weight of the plunger and valve. Then if at 
any moment pa exceeds w the plunger will rise, and if it is less than 
w the plunger will descend. Apart from friction, and assuming the 
valve D to be strictly an equilibrium valve, since 01 and w are 
constant, p must be constant also, and equal to w/oi. By making w 
small and w large, the difference of pressure required to ensure the 
working of the apparatus may be made very small. Valves working 
with a difference of pressure of \ in. of water have been constructed. 

VI. STEADY FLOW OF COMPRESSIBLE FLUIDS. 

§ 61. External Work during the Expansion of Air. — If air expands 
without doing any external work, its temperature remains constant. 

This result was first 
experimentally demon- 
strated by J. P. Joule. 
It leads to the conclu- 
sion that, however air 
changes its state, the in- 
ternal work done is pro- 
portional to the change 
of temperature. When, 
in expanding, air does 
work against an external 
resistance, either heat 
must be supplied or the 
temperature falls. 

To fix the conditions, 
suppose 1 lb of air con- 
fined behind a piston of 
I sq. ft. area (fig. 76). 
Let the initial pressure 
be pi and the volume of 
the air vi, and suppose 
this to expand to the 
pressure pt and volume 



\o. 






p,\ c Pi 




* V, -■* ; 

* ; v • ■•■-»; 

<• - ; v,--{-~ 




f 

EH 


! i 

: 1 



Fig. 76. 



»2- If p and v are the corresponding pressure and volume at any 
intermediate point in the expansion, the work done on the piston 
during the expansion from v to v+dv is pdv, and the whole work 
during the expansion from »i to » 2 , represented by the area abed, is 



Case 1. — So much heat is supplied to the air during expansion 
that the temperature remains constant. Hyperbolic expansion. 
Then pv—piVi. 

Work done during expansion per pound of air 



=fl[pdv=p 1 v 1 fl 



'dv/v 




Fig. 77. 






pdv. 



Amongst possible cases two may be selected. 



= £l!>l loge Vs/vi=piUi loge pi/pt. (i) 

Since the weight per cubic foot is the reciprocal of the volume per 
pound, this may be written 

(P1IG1) loge G1/G2. (10) 

Then the expansion curve ab is a common hyperbola. 

Case 2. — No heat is supplied to the air during expansion. Then 
the air loses an amount of heat equivalent to the external work done 
and the temperature falls. Adiabatic expansion. 

In this case it can be shown that 

pvy=piv{*, 
where 7 is the ratio of the specific heats of air at constant pressure 
and volume. Its value for air is 1-408, and for dry steam 1-135. 

Work done during expansion per pound of air. 

= flpdv = p l v l yfl°dvlvy 

= -{Ml?/(t-i)HiM?- 1 -iM v - 1 } 

= [?.w/(7-i)](iM y - 1 -iM'-'] 

= \PiV l /(y-i)}{i-(v 1 lvd y - 1 l (2) 

The value of piVi for any given temperature can be found from the 
data already given. 

As before, substituting the weights Gi, G 2 per cubic foot for the 
volumes per pound, we get for the work of expansion 

(i>./G,){i/(7-i)i fi-(G 2 /G 1 ) y - 1 !. (2a) 

=*Wi/(7-i)} [i-fa/pov-v/y]- (2b) 

§ 62. Modification of the Theorem of Bernoulli for the Case of a 
Compressible Fluid. — In the application of the principle of work to a 
filament of compressible fluid, the internal work done by the ex- 
pansion of the fluid, or absorbed 
in its compression, must be 
taken into account. Suppose, 
as before, that AB (fig. 77) 
comes to A'B' in a short time t. 
Let pi, Mi, Vi, Gi be the pres- 
sure, sectional area of stream, 
velocity and weight of a cubic 
foot at A, and p 2 , « 2 , v*, G2 the 
same quantities at B. Then, from the steadiness of motion, the 
weight of fluid passing A in any given time must be equal to the 
weight passing fi : 

GiioiVit = GzoizVzt. 
Let Zi, z 2 be the heights of the sections A and B above any given 
datum. Then the work of gravity on the mass AB in t seconds is 

Gia>iz>i<(zi — z 2 ) = W(zi — zi)t, 
where W is the weight of gas passing A or B per second. As in 
the case of an incompressible fluid, the work of the pressures on the 
ends of the mass AB is 

plQJlVit — p^tfl-it, 

= (pilGi-p 2 /G i Wt. 
The work done by expansion of Wi lb of fluid between A and B is 
W« f^pdv. The change of kinetic energy as before is (W/2g) (u 2 2 — »i 2 )f. 
Hence, equating work to change of kinetic energy, 

W(z 1 -z 2 )Z+(^i/G 1 -^/G 2 )W/+W<r^i> = (W/2g) W-vi*)t; 

.'. zi+Pi/Gi+vi' i J2g=z 2 +pVG 2 +v 2 y2g-p^pdv. (1) 

Now the work of expansion per pound of fluid has already been 
given. If the temperature is constant, we get (eq. ia, § 61) 

Zl+£l/Gl+»r72g=S2+£2/G 2 +Z> 2 72g-(£l/Gl) loge (G1/G2). 

But at constant temperature pi/Gi = £ 2 /G 2 ; 

/. Zi+»i 2 /2g = Z2-|-I>2 2 /2g-(£l/Gi) loge (pl/pz), 

or, neglecting the difference of level, 

(tf-l'l 2 )/2g = (^l/G 1 )loge (pi/pl). 

Similarly, if the expansion is adiabatic (eq. 2a, § 61), 
zi+pi/Gi -Hi 2 /2g = z 2 -r-fc/Gs +f2 2 /2g - (pi/Gi) 1 1 l(y - 1 ) j 

[i-(ptfpi)Wy\; 

or neglecting the difference of level 
W -tf )/2g = (A/G0[i +1/(7 - i){i - (frlpiW-viyft-ptlGi. 

It will be seen hereafter that there is a limit in the ratio pilpt beyond 
which these expressions cease to be true. 

§ 63. Discharge of Air from an Orifice.— The form of the equation 
of work for a steady stream of compressible fluid is 
Zi+WGi+!>i 2 /2g = Z2+£2/G2+%V2g-(£i/Gi){i/(7-i)} , , s/V „, , 



(2) 
(2a) 

(3) 
(30) 



FRICTION OF LIQUIDS] 



HYDRAULICS 



57 



the expansion being adiabatic, because in the flow of the streams of 
air through an orifice no sensible amount of heat can be communi- 
cated from outside. 

Suppose the air flows from a vessel, where the pressure is pi and 
the velocity sensibly zero, through an orifice, into a space where the 
pressure is pi. Let vt be the velocity of the jet at a point where the 
convergence of the streams has ceased, so that the pressure in the 
jet is also p 2 . As air is light, the work of gravity will be small 
compared with that of the pressures and expansion, so that Ziz 2 
may be neglected. Putting these values in the equation above — 

A/G 1 =/> 2 /G 2 +tf/2g-(A/G 1 )!i/(7-i)){i-(^2/A) (v - l)/Y ; 

^/2g = WG 1 -^/G 2 + (A/G 1 )(i/(T-i)){i-to/pi) (v - l)/Y ) 

= (?i/G 1 )!t/(t-i)-(^/A) 7 - i/v /(t-i)}-^/G 2 . 

But NU y = £2/W .-. fc/G 2 = fi>i/Gi)(p 2 /pi) (l '- l)/1 ' 

»iV2« = (fr/G,){7/(Y-l)} \i-(p2/Pi) iy ~ l)/y h (0 

or _ vi-/2g = [7/ (7 - 1) j j (pi/Gi) - (> 2 /G 2 )) ; 

an equation commonly ascribed to L. J. Weisbach (Civilingenieur, 
1856), though it appears to have been given earlier by A. J. C. Barre 
de Saint Venant and L. Wantzel. 

It has already (§ 9, eq. 4a) been seen that 
^/G I = (^„/Go)(7- 1 /r ) 
where for air £0 = 2116-8, Go = -o8o75 and 1-0 = 492-6. 

*<2 2 /2g = {/>oTi->7Goro(7-l)! \l-(p2/pi) (y - l)/y }; (2) 

or, inserting numerical values, 

»2 2 /2g = i83-6ti( i - (P2IP1) °- 29 | ; (20) 

which gives the velocity of discharge v 2 in terms of the pressure and 
absolute temperature, pi, n, in the vessel from which the air flows, 
and the pressure pi in the vessel into which it flows. 

Proceeding now as for liquids, and putting w for the area of the 
orifice and c for the coefficient of discharge, the volume of air dis- 
charged per second at the pressure pi and temperature t 2 is 

Q 2 = CM , 2 = c<0 V [(2g7M7- I)G,)(I - 0/fr) (y - l)/Y )] 

= loS-jco 1 ^[n\i-(p 2 lPir^)). (3) 

If the volume discharged is measured at the pressure pi and 
absolute temperature n in the vessel from which the air flows, let 
Qi be that volume ; then 

piQi y =p2QS; 
Qi = (ft/£i) l/Y Q2; 
Qi=cu V[{2g7M7-i)G 1 | \(p 1 /p0 2/y -(p2/Pi) iy+t)/y \]- 
Let (p2/pi) 2/y -(p-2lPi) {y - l)/y = (p2/piy n -(p2/Piy-'= + ; then 
Qi =coi V [2gypnpi{y — l)Gi] 

= lo8-7co>V(riiA). (4) 

The weight of air at pressure pi and temperature n is 

Gi =£1/53-2x1 lb per cubic foot. 

Hence the weight of air discharged is 

W = GiQi=cw V[2g7£iGi^/(7-i)] 

= 2-043c<op! V (<AM). (5) 

Weisbach found the following values of the coefficient of dis- 
charge c: — 

Conoidal mouthpieces of the form of the! 

contracted vein with effective pressures r c = 

of -23 to I- 1 atmosphere .... J 0-97 too-99 

Circular sharp-edged orifices .... 0-563 ,, 0-788 

Short cylindrical mouthpieces .... o-8l ,, 0-84 

The same rounded at the inner end . 0-92 ,, 0-93 

Conical converging mouthpieces . . . 0-90 ,, 0-99 

§ 64. Limit to the Application of the above Formulae. — In the 
formulae above it is assumed that the fluid issuing from the orifice 
expands from the pressure pi to the pressure £ 2 , while passing from 
the vessel to the section of the jet considered in estimating the area 
u. Hence p 2 is strictly the pressure in the jet at the plane of the 
external orifice in the case of mouthpieces, or at the plane of the 
contracted section in the case of simple orifices. Till recently it 
was tacitly assumed that this pressure pi was identical with the 
general pressure external to the orifice. R. D. Napier first discovered 
that, when the ratio P2IP1 exceeded a value which does not greatly 
differ from 0-5, this was no longer true. In that case the expansion 
of the fluid down to the external pressure is not completed at the 
time it reaches the plane of the contracted section, and the pressure 
there is greater than the general external pressure; or, what amounts 
to the same thing, the section of the jet where the expansion is com- 
pleted is a section which is greater than the area c c a of the contracted 
section of the jet, and may be greater than the area a of the orifice. 
Napier made experiments with steam which showed that, so long as 
ptlpi>0'5t the formulae above were trustworthy, when pi was taken 
to be the general external pressure, but that, if pi/pi<o-5, then the 
pressure at the contracted section was independent of the external 
pressure and equal to o-$pi. Hence in such cases the constant value 
0-5 should be substituted in the formulae for the ratio of the internal 
and external pressures pi/pi. 



It is easily deduced from Weisbach's theory that, if the pressure 
external to an orifice is gradually diminished, the weight of air dis- 
charged per second increases to a maximum for a value of the ratio 
p2/Pi={2/(y + i)\ y - l/y 
= 0-527 for air 
= 0-58 for dry steam. 
For a further decrease of external pressure the discharge diminishes, 
— a result no doubt improbable. The new view of Weisbach's 
formula is that from the point where the maximum is reached, or 
not greatly differing from it, the pressure at the contracted section 
ceases to diminish. 

A. F. Fliegner showed {Civilingenieur xx., 1874) that for air flow- 
ing from well-rounded mouthpieces there is no discontinuity of the 
law of flow, as Napier's hypothesis implies, but the curve of flow 
bends so sharply that Napier's rule may be taken to be a good 
approximation to the true law. The limiting value of the ratio 
P2IP1, for which Weisbach's formula, as originally understood, ceases 
to apply, is for air 0-5767; and this is the number to be substituted 
for pilpi in the formulae when P2/P1 falls below that value. For later 
researches on the flow of air, reference may be made to G. A. Zeuner's 
paper (Civilingenieur, 1871), and Fliegner's papers (ibid., 1877, 
1878). 

VII. FRICTION OF LIQUIDS. 

§ 65. When a stream of fluid flows over a solid surface, or con- 
versely when a solid moves in still fluid, a resistance to the motion 
is generated, commonly termed fluid friction. It is due to the vis- 
cosity of the fluid, but generally the laws of fluid friction are very 
different from those of simple viscous resistance. It would appear 
that at all speeds, except the slowest, rotating eddies are formed by 
the roughness of the solid surface, or by abrupt changes of velocity 
distributed throughout the fluid; and the energy expended in pro- 
ducing these eddying motions is gradually lost in overcoming the 
viscosity of the fluid in regions more or less distant from that where 
they are first produced. 

The laws of fluid friction are generally stated thus : — 

1. The frictional resistance is independent of the pressure between 
the fluid and the solid against which it flows. This may be verified 
by a simple direct experiment. C. H. Coulomb, for instance, oscil- 
lated a disk under water, first with atmospheric pressure acting on 
the water surface, afterwards with the atmospheric pressure removed. 
No difference in the rate of decrease of the oscillations was observed. 
The chief proof that the friction is independent of the pressure is 
that no difference of resistance has been observed in water mains 
and in other cases, where water flows over solid surfaces under widely 
different pressures. 

2. The frictional resistance of large surfaces is proportional to the 
area of the surface. 

3. At low velocities of not more than 1 in. per second for water, 
the frictional resistance increases directly as the relative velocity of 
the fluid and the surface against which it flows. At velocities of 
I ft. per second and greater velocities, the frictional resistance is 
more nearly proportional to the square of the relative velocity. 

In many treatises on hydraulics it is stated that the frictional 
resistance is independent of the nature of the solid surface. The 
explanation of this was supposed to be that a film of fluid remained 
attached to the solid surface, the resistance being generated between 
this fluid layer and layers more distant from the surface. At ex- 
tremely low velocities the solid surface docs not seem to have much 
influence on the friction. In Coulomb's experiments a metal surface 
covered with tallow, and oscillated in water, had exactly the same 
resistance as a clean metal surface, and when sand was scattered over 
the tallow the resistance was only very slightly increased. The 
earlier calculations of the resistance of water at higher velocities in 
iron and wood pipes and earthen channels seemed to give a similar 
result. These, however, were erroneous, and it is now well understood 
that differences of roughness of the solid surface very greatly influ- 
ence the friction, at such velocities as are common in engineering 
practice. H. P. G. Darcy's experiments, for instance, showed that 
in old and incrusted water mains the resistance was twice or some- 
times thrice as great as in new and clean mains. 

§ 66. Ordinary Expressions for Fluid Friction at Velocities not 
Extremely Small. — Let / be the frictional resistance estimated in 
pounds per square foot of surface at a velocity of 1 ft. per second; 
« the area of the surface in square feet; and v its velocity in feet 
per second relatively to the water in which it is immersed. Then, 
in accordance with the laws stated above, the total resistance of the 
surface is 

R =/W (1) 

where / is a quantity approximately constant for any given surface. 

I=2«//G, 

R = fG&>i> 2 /2g, (2) 

where £ is, like /, nearly constant for a given surface, and is termed 
the coefficient of friction. 

The following are average values of the coefficient of friction for 
water, obtained from experiments on large plane surfaces, moved in 
an indefinitely large mass of water. 



5» 



HYDRAULICS 



[FRICTIONlOF LIQUIDS 





Coefficient 

of Friction, 

I 


Frictional 

Resistance in 

lb per sq. ft. 

/ 


New well-painted iron plate . 
Painted and planed plank (Beaufoy) 
Surface of iron ships (Rankine) . 
Varnished surface (Froude) . 
Fine sand surface ,, ... 
Coarser sand surface ,, . 


•00489 
•00350 
•00362 
•00258 
•00418 
•00503 


•00473 
•00339 
•00351 
•00250 
•00405 
•00488 



The distance through which the frictional resistance is overcome 
is r ft. per second. The work expended in fluid friction is therefore 
given by the equation — 

Work expended =/wi> 3 foot-pounds per second ( (3). 

= £Guv 3 /2g „ ,, ] 

The coefficient of friction and the friction per square foot of 
surface can be indirectly obtained from observations of the discharge 
of pipes and canals. In obtaining them, however, some assumptions 
as to the motion of the water must be made, and it will be better 
therefore to discuss these values in connexion with the cases to 
which they are related. 

Many attempts have been made to express the coefficient of 
friction in a form applicable to low as well as high velocities. The 
older hydraulic writers considered the 
resistance termed fluid friction to be 
made up of two parts, — a part due 
directly to the distortion of the mass of 
water and proportional to the velocity 
of the water relatively to the solid sur- 
face, and another part due to kinetic 
energy imparted to the water striking 
the roughnesses of the solid surface and 
proportional to the square of the 
velocity. Hence they proposed to take 

| = o+/3/o 

in which expression the second term is 

of greatest importance at very low == _____^_____ 

velocities, and of comparatively little k^JJ^jJ^^^s^g^-sMJ 

importance at velocities over about j ft. r— 

per second. Values of £ expressed in this ~_Z 

and similar forms will be given in con- ; i^S» A 

nexion with pipes and canals. ■ 

All these expressions must at present 1 - 

be regarded as merely empirical ex- ;_~ ' ~ 

pressions serving practical purposes. — — ■ — • — — — - 

The frictional resistance will be seen' 
to vary through wider limits than these 

expressions allow, and to depend on circumstances of which they do 
not take account. 

§ 67. Coulomb's Experiments. —The first direct experiments on 
fluid friction were made by Coulomb, who employed a circular disk 
suspended by a thin brass wire and oscillated in its own plane. His 
experiments were chiefly made at very low velocities. When the 
disk is rotated to any given angle, it oscillates under the action of its 
inertia and the torsion of the wire. The oscillations diminish 
gradually in consequence of the work done in overcoming the friction 
of the disk. The diminution furnishes a means of determining the 
friction. 

Fig. 78 shows Coulomb's apparatus. LK supports the wire and 
disk; ag is the brass wire, the torsion of which causes the oscilla- 
tions ; DS is a graduated 
disk serving to measure 
the angles through which 
the apparatus oscillates. 
To this the friction disk 
is rigidly attached hang- 
ing in a vessel of water. 
The friction disks were 
from 4-7 to 7-7 in. dia- 
meter, and they gener- 
ally made one oscillation 
in from 20 to 30 seconds, 
through angles varying 
from 360° to 6°. When 
the velocity of the cir- 
cumference of the disk 
was less than 6 in. per 
second, the resistance 
was sensibly propor- 
tionalto the velocity. 
Beaufoy' s Experiments. — Towards the end of the 18th century 
Colonel Mark Beaufoy (1 764-1 827) made an immense mass of 
experiments on the resistance of bodies moved through water 
(Nautical and Hydraulic Experiments, London, 1834). Of these the 
only ones directly bearing on surface friction were some made in 1796 
and 1798. Smooth painted planks were drawn through water and 



the resistance measured. For two planks differing in area by 46 sq. 
ft., at a velocity of 10 ft. per second, the difference of resistance, 
measured on the difference of area, was 0-339 lb per square foot. 
Also the resistance varied as the 1 -949th power of the velocity. 

§ 68. Froude's Experiments. — The most important direct experi- 
ments on fluid friction at ordinary velocities are those made by 
William Froude (1810-1879) at Torquay. The method adopted in 
these experiments was to tow a board in a still water canal, the 
velocity and the resistance being registered by very ingenious re- 
cording arrangements. The general arrangement of the apparatus is 
shown in fig. 79. AA is the board the resistance of which is to be 
determined. B is a cut-water giving a fine entrance to the plane 
surfaces of the board. CC is a bar to which the board AA is attached, 
and which is suspended by a parallel motion from a carriage running 
on rails above the still water canal. G is a link by which the re- 
sistance of the board is transmitted to a spiral spring H. A bar I 
rigidly connects the other end of the spring to the carriage. The 
dotted lines K, L indicate the position of a couple of levers by which 
the extension of the spring is caused to move a pen M, which records 
the extension on a greatly increased scale, by a line drawn on the 
paper cylinder N. This cylinder revolves at a speed proportionate 
to that of the carriage, its motion being obtained from the axle of the 
carriage wheels. A second pen O, receiving jerks at every second 
and a quarter from a clock P, records time on the paper cylinder. 
The scale for the line of resistance is ascertained by stretching the 
spiral spring by known weights. The boards used for the experiment 





Fig. 78. 



Fig. 79. 

were ^ in. thick, 19 in. deep, and from I to 50 ft. in length, cutwater 
included. A lead keel counteracted the buoyancy of the board. 
The boards were covered with various substances, such as paint, 
varnish, Hay's composition, tinfoil, &c, so as to try the effect of 
different degrees of roughness of surface. The results obtained by 
Froude may be summarized as follows : — 

1. The friction per square foot of surface varies very greatly for 
different surfaces, being generally greater as the sensible roughness 
of the surface is greater. Thus, when the surface of the board was 
covered as mentioned below, the resistance for boards 50 ft. long, 
at 10 ft. per second, was— 

Tinfoil or varnish 0-25 fb per sq. ft. 

Calico 0-47 ,, ,, 

Fine sand 0-405 ,, ,, 

Coarser sand 0-488 ,, ,, 

2. The power of the velocity to which the friction is proportional 
varies for different surfaces. Thus, with short boards 2 ft. long, 

For tinfoil the resistance varied as v 2,16 . 

For other surfaces the resistance varied as v i,ta . 
With boards 50 ft. long, 

For varnish or tinfoil the resistance varied as t 4 " 83 . 
For sand the resistance varied as t> 2 ' ra . 

3. The average resistance per square foot of surface was much 
greater for short than for long boards; or, what is the same thing; 
the resistance per square foot at the forward part of the board was 
greater than the friction per square foot of portions more sternward. 
Thus, 

Mean Resistance in 
lb per sq . ft. 
Varnished surface . . 2 ft. long 0-41 

50 „ 0-25 

Fine sand surface . . 2 ,, o-8l 

50 ,, 0-405 

This remarkable result is explained thus by Froude : " The 
portion of surface that goes first in the line of motion, in experiencing 
resistance from the water, must in turn communicate motion to the 
water, in the direction in which it is itself travelling. Consequently 



STEADY FLOW IN PIPES] 



HYDRAULICS 



59 



the portion of surface which succeeds the first will be rubbing, not 
against stationary water, but against water partially moving in its 
owrl direction, and cannot therefore experience so much resistance 
from it." 

§ 69. The following table gives a general statement of Froude's 
results. In all the experiments in this table, the boards had a fine 
cutwater and a fine stern end or run, so that the resistance was 
entirely due to the surface. The table gives the resistances per 
square foot in pounds, at the standard speed of 600 feet per minute, 
and the power of the speed to which the friction is proportional, so 
that the resistance at other speeds is easily calculated. 





Length of Surface, or Distance from Cutwater, in feet. 


2 ft. 


8 ft. 


20 ft. 


50 ft. 


A 


B 


C 


A 


B 


C 


A 


B 


C 


A 


B 


C 


Varnish 

Paraffin 
1 Tinfoil 
I Calico 
! Fine sand 

Medium sand 

Coarse sand . 


2-00 
2-l6 

i-93 

2-O0 
2-00 
2-00 


•41 
•38 
•30 
•87 
•81 
•90 

I-IO 


•390 
•37° 
•295 
725 
•690 

•730 
•880 


1-85 
1-94 
1-99 
1-92 

2-00 
2-00 
2-00 


•325 
•3H 
•278 
■626 
•583 
•625 
■714 


•264 
•260 
•263 
•504 
■450 
•488 
•520 


1-85 
1-93 
1-90 
1-89 

2-00 
2-00 
2-00 


•278 

•271 
•262 

•S3i 
•480 

•534 
•588 


•240 
•237 
•244 
•447 
•3"84 
•465 
•490 


1-83 

1 -83 
1-87 

2-06 
2-00 


•250 

•246 
•474 
•405 

•488 


•226 

•232 
•423 
•337 
•456 



Columns A give the power of the speed to which the resistance is 
approximately proportional. 

Columns B give the mean resistance per square foot of the whole 
surface of a board of the lengths stated in the table. 

Columns C give the resistance in pounds of a square foot of surface 
at the distance sternward from the cutwater stated in the heading. 

Although these experiments do not directly deal with surfaces of 
greater length than 50 ft., they indicate what would be the resistances 
of longer surfaces. For at 50 ft. the decrease of resistance for an 
increase of length is so small that it will make no very great difference 
in the estimate of the friction whether we suppose it to continue to 
diminish at the same rate or not to diminish at all. For a varnished 
surface the friction at 10 ft. per second diminishes from 0-41 to 0-32 
ft per square foot when the length is increased from 2 to 8 ft., but it 
only diminishes from 0-278 to 0-250 lb per square foot for an increase 
from 20 ft. to 50 ft. 

If the decrease of friction sternwards is due to the generation of a 
current accompanying the moving plane, there is not at first sight 
any reason why the decrease should not be greater than that shown 
by the experiments. The current accompanying the board might be 
assumed to gain in volume and velocity sternwards, till the velocity 
was nearly the same as that of the moving plane and the friction per 
square foot nearly zero. That this does not happen appears to be due 
to the mixing up of the current with the still water surrounding it. 
Part of the water in contact with the board at any point, and receiv- 
ing energy of motion from it, passes afterwards to distant regions of 
still water, and portions of still water are fed in towards the board 
to take its place. In the forward part of the board more kinetic 
energy is given to the current than is diffused into surrounding space, 
and the current gains in velocity. At a greater distance back there is 
an approximate balance between the energy communicated to the 
water and that diffused. The velocity of the current accompanying 
the board becomes constant or nearly constant, and the friction per 
square foot is therefore nearly constant also. 

§ 70. Friction of Rotating Disks. — A rotating disk is virtually a 
surface of unlimited extent and it is convenient for experiments on 
friction with different surfaces at different speeds. Experiments 
carried out by Professor W. C. LTnwin {Proc. Inst. Civ. Eng. lxxx.) 
are useful both as illustrating the laws of fluid friction and as giving 
data for calculating the resistance of the disks of turbines and 
centrifugal pumps. Disks of 10, 15 and 20 in. diameter fixed on a 
vertical shaft were rotated by a belt driven by an engine. They were 
enclosed in a cistern of water between parallel top and bottom fixed 
surfaces. The cistern was suspended by three fine wires. The friction 
of the disk is equal to the tendency of the cistern to rotate, and this 
was measured by balancing the cistern by a fine silk cord passing over 
a pulley and carrying a scale pan in which weights could be placed. 

If w is an element of area on the disk moving with the velocity v, 
the friction on this element is fun", where / and n arc constant for 
any given kind of surface. Let a be the angular velocity of rotation, 
K the radius of the disk. Consider a ring of the surface between rand 
r+dr. Its area is 2ivrdr, its velocity ar and the friction of this ring 
is f2irrdra"r n . The moment of the friction about the axis of rotation 
is 2ira"fr" + -dr, and the total moment of friction for the two sides of 
the disk is 

M = ^Ijfr^dr = |4*-a»/(» +3) !/R n+3 - 
If N is the number of revolutions per sec, 

M = 52"«7r»+ 1 N"/(n+3)!/R»« l 
and the work expended in rotating the disk is 

Ma = !2" +3 7r" +2 N" +1 /(«+3)!/R" +3 foot lb per sec. 
The experiments give directly the values of M for the disks corre- 



sponding to any speed N. From these the values of/ and n can be 
deduced, / being the friction per square foot at unit velocity. For 
comparison with Froude's results it is convenient to calculate the 
resistance at 10 ft. per second, which is F=/io". 

The disks were rotated in chambers 22 in. diameter and 3, 6 and 
12 in. deep. In all cases the friction of the disks increased a little 
as the chamber was made larger. This is probably due to the stilling 
of the eddies against the surface of the chamber and the feeding back 
of the stilled water to the disk. Hence the friction depends not only 
on the surface of the disk but to some extent on the surface of the 
chamber in which it rotates. If the surface of the chamber is made 
rougher by covering with coarse sand there is 
also an increase of resistance. 

For the smoother surfaces the friction varied 
as the 1 -85th power of the velocity. For the 
rougher surfaces the power of the velocity to 
which the resistance was proportional varied 
from 1-9 to 2-1. This is in agreement with 
Froude's results. 

Experiments with a bright brass disk showed 
that the friction decreased with increase of 
temperature. The diminution between 41 
and 130° F. amounted to 18%. In the general 
equation M =cN" for any given disk, 

Ct=o-i328(i — 0-002I(), 
where c t is the value of c for a bright brass 
disk 0-85 ft- i n diameter at a temperature t° F. 
The disks used were either polished or made rougher by varnish 
or by varnish and sand. The following table gives a comparison of 
the results obtained with the disks and Froude's results on planks 
50 ft. long. The values given are the resistances per square foot at 
10 ft. per sec. 

Froude's Experiments. 
Tinfoil surface . . 0-232 

Varnish 0-226 

Fine sand .... 0-337 
Medium sand . . 0-456 



Disk Experiments. 
Bright brass . 0-202 to 0-229 
Varnish . . 0-220 to 0-233 
Fine sand °'339 

Very coarse sand 0-587 to 0-715 



'-dl 



VIII. STEADY FLOW OF WATER IN PIPES OF 
UNIFORM SECTION. 

§ 71. The ordinary theory of the flow of water in pipes, on which 
all practical formulae are based, assumes that the variation of velocity 
at different points of any cross section may be neglected. The 
water is considered as moving in plane layers, which are driven 
through the pipe against the frictional resistance, by the difference 
of pressure at or elevation of the ends of the pipe. If the motion 
is steady the velocity at each cross section remains the same from 
moment to moment, and if the cross sectional area is constant the 
velocity at all sections must be the same. Hence the motion is 
uniform. The most important resistance to the motion of the water 
is the surface friction of the pipe, and it is convenient to estimate 
this independently of some smaller resistances which will be ac- 
counted for presently. 

In any portion of a uniform pipe, excluding for the present the 
ends of the pipe, the water enters and leaves at the same velocity. 
For that portion there- 
fore the work of the 
external forces and of 
the surface friction 
must be equal. Let 
fig. 80 represent a very 
short portion of the 
pipe, of length dl, be- 
tween cross sections at 
2 and z-\-dz ft. above 
any horizontal datum 
line xx, the pressures at 

the cross Sections being -~ A ^" V 

p and p+dp lb per ' 

square foot. Further, p g 

let Q be the volume of 

flow or discharge of the pipe per second, it the area of a norma! 

cross section, and x the perimeter of the pipe. The Q cubic feet, 

which flow through the space considered per second, weigh GQ lb, 

and fall through a height — dz ft. The work done by gravity is then 

-GQ<fe; 
a positive quantity if dz is negative, and vice versa. The resultant 
pressure parallel to the axis of the pipe is p — {p-\~dp) = —dp lb per 
square foot of the cross section. The work of this pressure on the 
volume Q is 

-Qdp. 
The only remaining force doing work on the system is the friction 
against the surface of the pipe. The area of that surface is % dl. 

The work expended in overcoming the frictional resistance per 
second is (see § 66, eq. 3) 

-ZGxdlv'l2g, 
or, since Q — Qv, 

-rG(x/n)Q(* ! /2, ? )tf7; 




6o 



HYDRAULICS 



[STEADY FLOW IN PIPES 



the negative sign being taken because the work is done against a 
resistance. Adding all these portions of work, and equating the 
result to zero, since the motion is uniform, — 

-GQdz-Qdp-t;G(xln)Q(vV2g)dl=o. 
Dividing by GQ, 

dz+dp/G+UxM(v-/2g)dl = o. 
Integrating, 

z+pi'G +r(x/Q) 2 /2g)/ = constant. (i) 

§ 72. Let A and B (fig. 81) be any two sections of the pipe for 
which p, z, / have the values pi, z lt h, and pi, z 2 , h, respectively. 
Then 

zi +PJG + f (x/Q) (vV2g)h = Z2 +P2/G + f (x/o) (» 2 /2g)4 ; 

or, if h—h=L, rearranging the terms, 

r^/2g = (i/L)((z 1 +pi/G)-(z 2 +^/G)}n/ x . (2) 

Suppose pressure columns introduced at A and B. The water will 
rise in those columns to the heights pi/G and pzjG due to the 




Fig. 81. 

pressures pi and p-i at A and B. Hence (zi+pi/G) — (z 2 +p 2 /G) is 
the quantity represented in the figure by DE, the fall of level of 
the pressure columns, or virtual fall of the pipe. If there were no 
friction in the pipe, then by Bernoulli's equation there would be no 
fall of level of the pressure columns, the velocity being the same at 
A and B. Hence DE or h is the head lost in friction in the distance 
AB. The quantity DE/AB=/t/L is termed the virtual slope of 
the pipe or virtual fall per foot of length. It is sometimes termed 
very conveniently the relative fall. It will be denoted by the 
symbol i. 

The quantity fi/x which appears in many hydraulic equations is 
called the hydraulic mean radius of the pipe. It will be denoted 
by m. 

Introducing these values, 



f v-hg = mh/L = mi. 
For pipes of circular section, and diameter d, 
m = il/x = {ird 2 /ird = \d. 



Then 
or 



Wl2g = \dhlL=\di; 
fc = r(4L/W/2g); 



(3) 



(4) 
(4a) 



which shows that the head lost in friction is proportional to the 
head due to the velocity, and is found by multiplying that head by 
the coefficient 4fL/d. It is assumed above that the atmospheric 
pressure at C and D is the same, and this is usually nearly the case. 
But if C and D are at greatly different levels the excess of baro- 
metric pressure at C, in feet of water, must be added to pi/G. 

§ 73. Hydraulic Gradient or Line of Virtual Slope. — Jo'n CD. 
Since the head lost in friction is proportional to L, any intermediate 
pressure column between A and B will have its free surface on the 
line CD, and the vertical distance between CD and the pipe at any 
point measures the pressure, exclusive of atmospheric pressure, in 
the pipe at that point. If the pipe were laid along the line CD 
instead of AB, the water would flow at the same velocity by gravity 
without any change of pressure from section to section. Hence CD 
is termed the virtual slope or hydraulic gradient of the pipe . It is 
the line of free surface level for each point of the pipe. 

If an ordinary pipe, connecting reservoirs open to the air, rises at 
any joint above the line of virtual slope, the pressure at that point 
is less than the atmospheric pressure transmitted through the pipe. 
At such a point there is a liability that air may be disengaged from 
the water, and the flow stopped or impeded by the accumulation of 
air. If the pipe rises more than 34 ft. above the line of virtual slope, 
the pressure is negative. But as this is impossible, the continuity 
of the flow will be broken. 

If the pipe is not straight, the line of virtual slope becomes a 
curved line, but since in actual pipes the vertical alterations of level 
are generally small, compared with the length of the pipe, distances 
measured along the pipe are sensibly proportional to distances 



measured along the horizontal projection of the pipe. Hence the 
line of hydraulic gradient may be taken to be a straight line without 
error of practical importance. * 

§ 74. Case of a Uniform Pipe connecting two Reservoirs, when all the 
Resistances are taken into account. — Let h (fig. 82) be the difference 
of level of the reservoirs, and v the velocity, in a pipe of length L 
and diameter d. The whole work done per second is virtually the 
removal of Q cub. ft. of water from the surface of the upper 
reservoir to the surface of the lower reservoir, that is GQh foot- 
pounds. This is expended in three ways. (1) The head i^/2g, corre- 
sponding to an expenditure of GQi» 2 /2g foot-pounds of work, is 
employed in giving energy of motion to the water. This is ulti- 

( i+ £}_fl -.-'■ 



J- 



-*!>!*__<? Virtual Sl , » 




(5) 



Fig. 82. 

mately wasted in eddying motions in the lower reservoir. (2) A 
portion of head, which experience shows may be expressed in the 
form foi' 2 /2g, corresponding to an expenditure of GQ£aP/2g foot- 
pounds of work, is employed in overcoming the resistance at the 
entrance to the pipe. (3) As already shown the head expended in 
overcoming the surface friction of the pipe is f (4L/tf") (» 2 /2g) correspond- 
ing to GQf(4L/J)(» 2 / 2 g) foot-pounds of work. Hence 

GQA = GQ^/2g+GQfo^/2g+GQr.4L.» 2 /rf.2g; 

^=(i+fo+f.4L,«y/2g. ? 

tr = 8-025V[Ad/{(i+fo)d+4fL)]. J 

If the pipe is bellmouthed, f is about = -08. If the entrance to 
the pipe is cylindrical, £0 = 0-505. Hence i+f =i-o8 to 1-505. 
In general this is so small compared with f4L/d that, for practical 
calculations, it may be neglected; that is, the losses of head other 
than the loss in surface friction are left out of the reckoning. It 
is only in short pipes and at high velocities that it is necessary to 
take account of the first two terms in the bracket, as well as the 
third. For instance, in pipes for the supply of turbines, v is usually 
limited to 2 ft. per second, and the pipe is bellmouthed. Then 
I- o8v 2 /2g =0-067 ft. In pipes for towns' supply v may range from 
2 to 4J ft. per second, and then i-5» 2 /2g = o-i to 0-5 ft. In either 
case this amount of head is small compared with the whole virtual 
fall in the cases which most commonly occur. 

When d and v or d and h are given, the equations above are solved 
quite simply. When v and h are given and d is required, it is better 
to proceed by approximation. Find an approximate value of d by 
assuming a probable value for f as mentioned below. Then from 
that value of d find a corrected value for f and repeat the calculation. 

The equation above may be put in the form 

A = (4f/d)[((i+foW4f}+L]^/2g; (6) 

from which it is clear that the head expended at the mouthpiece is 
equivalent to that of a length 

(i+r )d/4f 

of the pipe. Putting l+? = 1-505 and f = o-oi, the length of pipe 
equivalent to the mouthpiece is 37-6 d nearly. This may be added 
to the actual length of the pipe to allow for mouthpiece resistance 
in approximate calculations. 

§ 75. Coefficient of Friction for Pipes discharging Water. — From the 
average of a large number of experiments, the value of f for ordinary 
iron pipes is 

$- = 0-007567. (7) 

But practical experience shows that no single value can be taken 
applicable to very different cases. The earlier hydraulicians occupied 
themselves chiefly with the dependence of f on the velocity. Having 
regard to the difference of the law of resistance at very low and 
at ordinary velocities, they assumed that f might be expressed in the 
form 

f = a-|-0/t'. 
The following are the best numerical values obtained for f so ex- 
pressed : — 





a 


. 


R. de Prony (from 51 experiments) 

J. F. d'Aubuisson de Voisins 

J. A. Eytelwein 


0-006836 

0-00673 

0-005493 


o-ooin6 

0-001211 

0-00143 



Weisbach proposed the formula 

4f = a+ff/tl v = 0-003598 +0-004289/-^ v. 



(8) 



STEADY FLOW IN PIPES] 



HYDRAULICS 



61 



§ 76. Darcy's Experiments on Friction in Pipes. — All previous 
experiments on the resistance of pipes were superseded by the re- 
markable researches carried out by H. P. G. Darcy (1803-185&), the 
Inspector-General of the Paris water works. His experiments were 
carried out on a scale, under a variation of conditions, and with a 
degree of accuracy which leaves little to be desired, and the results 
obtained are of very great practical importance. These results may 
be stated thus : — 

1. For new and clean pipes the friction varies considerably with 
the nature and polish of the surface of the pipe. For clean cast 
iron it is about 1 J times as great as for cast iron covered with pitch. 

2. The nature of the surface has less influence when the pipes 
are old and incrusted with deposits, due to the action of the water. 
Thus old and incrusted pipes give twice as great a frictional resist- 
ance as new and clean pipes. Darcy's coefficients were chiefly 
determined from experiments on new pipes. He doubles these co- 
efficients for old and incrusted pipes, in accordance with the results 
of a very limited number of experiments on pipes containing incrus- 
tations and deposits. 

3. The coefficient of friction may be expressed in the form 
f = a + 0/v; but in pipes which have been some time in use it is 
sufficiently accurate to take f = oi simply, where ai depends on the 
diameter of the pipe alone, but a and on the other hand depend 
both on the diameter of the pipe and the nature of its surface. The 
following are the values of the constants. 

For pipes which have been some time in use, neglecting the term 
depending on the velocity ; 

f = o(l+/9/d). (9) 



For drawn wrought-iron or smooth cast- 
iron pipes 

For pipes altered by light incrustations 



•004973 
•00996 







•084 
•084 



These coefficients may be put in the following very simple form, 
without sensibly altering their value : — 



For clean pipes f = '005(1 + i/l2d) 

For slightly incrusted pipes . f =-oi(i + i/l2(J) 



(9a) 



Darcy's Value of the Coefficient of Friction 
than 4 in. per second. 



f for Velocities not less 



Diameter 

of Pipe 

in Inches. 


f 


Diameter 

of Pipe 
in Inches. 


r 


New 
Pipes. 


Incrusted 
Pipes. 


New 
Pipes. 


Incrusted 
Pipes. 


2 
3 
4 
5 
6 

7 
8 

9 
12 

15 


0-00750 
•00667 
■00625 
■00600 
■00583 
•00571 
•00563 
■00556 
■00542 
•O0533 


0-01500 

•01333 
•01250 
•01200 
•01 167 
•01 143 
•01 125 

•OIIII 

•01083 
•01067 


18 
21 
24 
27 
30 
36 
42 
48 

54 


•00528 
•00524 
•00521 
•00519 
•00517 
•00514 
•00512 
•00510 
•00509 


•01056 
•01048 
•01042 
•01037 
•01033 
•01028 
•01024 
•0102 1 
•01019 



even selected experiments the values of the empirical coefficient f 
range from 0-16 to 0-0028 in different cases. Hence means of dis- 
criminating the probable value of f are necessary in using the equa- 
tions for practical purposes. To a certain extent the knowledge that 
f decreases with the size of the pipe and increases very much with 
the roughness of its surface is a guide, and Darcy's method of deal- 
ing with these causes of variation is very helpful. But a further 
difficulty arises from the discordance of the results of different ex- 
periments. For instance F. P. Stearns and J. M. Gale both experi- 
mented on clean asphalted cast-iron pipes, 4 ft. in diameter. Ac- 
cording to one set of gaugings f =-0051, and according to the other 
f = -0031. It is impossible in such cases not to suspect some error in 
the observations or some difference in the condition of the pipes not 
noticed by the observers. 

It is not likely that any formula can be found which will give 
exactly the discharge of any given pipe. For one of the chief factors 
in any such formula must express the exact roughness of the pipe 
surface, and there is no scientific measure of roughness. The most 
that can be done is to limit the choice of the coefficient for a pipe 
within certain comparatively narrow limits. The experiments on 
fluid friction show that the power of the velocity to which the 
resistance is proportional is not exactly the square. Also in deter- 
mining the form of his equation for f Darcy used only eight out of his 
seventeen series of experiments, and there is reason to think that some 
of these were exceptional. Barre de Saint-Venant was the first to 
propose a formula with two constants, 
dh\al = mV", 

where m and n are experimental constants. If this is written in the 
form 

log m-j-n log w = log (dh/41), 

we have, as Saint-Venant pointed out, the equation to a straight 
line, of which m is the ordinate at the origin and n the ratio of the 
slope. If a series of experimental values are plotted logarithmically 
the determination of the constants is reduced to finding the straight 
line which most nearly passes through the plotted points. Saint- 
Venant found for n the value of 1-71. In a memoir on the influence 
of temperature on the movement of water in pipes (Berlin, 1854) by 
G. H. L. Hagen (1797-1884) another modification of the Saint-Venant 
formula was given. This is h/l = mv n /d', which involves three ex- 
perimental coefficients. Hagen found » = i-75; x = i-25; and m 
was then nearly independent of variations of v and d. But the range 
of cases examined was small. In a remarkable paper in the Trans. 
Roy. Soc, 1883, Professor Osborne Reynolds made much clearer the 
change from regular stream line motion at low velocities to the 
eddying motion, which occurs in almost all the cases with which the 
engineer has to deal. Partly by reasoning, partly by induction 
from the form of logarithmically plotted curves of experimental 
results, he arrived at the general equation hll = c{v n ld 3 ~")V~ n , 
where n — \ for low velocities and n — 1-7 to 2 for ordinary velocities. 
P is a function of the temperature. Neglecting variations of tempera- 
ture Reynold's formula is identical with Hagen's if x = 3~». For 
practical purposes Hagen's form is the more convenient. 

Values of Index of Velocity. 



These values of f are, however, not exact for widely differing 
velocities. To embrace all cases Darcy proposed the expression 



f = (a+a 1 /d) + (^+A/(i 2 )/f; 



(10) 



which is a modification of Coulomb's, including terms expressing the 
influence of the diameter and of the velocity. For clean pipes Darcy 
found these values 

a = -004346 

ai = -0003992 

(3 =-0010182 

ft = -000005205. 

It has become not uncommon to calculate the discharge of pipes 
by the formula of E. Ganguillet and W. R. Kutter, which will be 
discussed under the head of channels. For the value of c in the 
relation v = cV {mi), Ganguillet and Kutter take 

4i-6 + i-8ii/n + -oo28i/t 

c_ l+[(4i-6-r--0O28i/i)(«/V»w)] 

where n is a coefficient depending only on the roughness of the pipe. 
For pipes uncoated as ordinarily laid » = o-oi3. The formula is very 
cumbrous, its form is not rationally justifiable and it is not at all 
clear that it gives more accurate values of the discharge than simpler 
formulae. 

§ 77. Later Investigations on Flow in Pipes. — The foregoing state- 
ment gives the theory of flow in pipes so far as it can be put in a 
simple rational form. But the conditions of flow are really more 
complicated than can be expressed in any rational form. Taking 



Surface of Pipe. 



Authority. 



Tin plate 

Wrought iron (gas 
Pipe) 

Lead .... 

Clean brass 

Asphalted 

Riveted wrought 
iron 

Wrought iron (gas 
Pipe) 



New cast iron 



Cleaned cast iron 



Incrusted cast iron 



Bossut . 
Hamilton Smith 



Darcy . 

Mair . . . 
Hamilton Smith 
Lampe . 
W. W. Bonn 
Stearns . 

Hamilton Smith 



Darcy 



Darcy 



Darcy 



Darcy 




62 



HYDRAULICS 



[STEADY FLOW IN PIPES 



I | ■ -- .; -B IT 


.fell ,*-'*^ . +* ■ - 


s' '■''* 


•4 i* f ,, ■ *s S ...r, 


± .J^c^^g: *. 


_4_ - - ■ ■■ ■ >• - v**~'iy**' r>V s* ■ 






~1 ^^'f^'^C^ 1 y^ xPs J? 


j - pr" J ' ^^ s\°> j X 


—L J^.—^^^k,^ 


— — ^' wOV \rf-T J 1 ^ 


^' 4I$»L^l_ /" 


it ^^^Jgfe^^te'' 


' " ^" ^^qj^: 


^ ^Sfc d^< 


^^%^^ iga? 


^ _^<^L^ l 








•5 ft^" „-^^ -^ 


,^? 6 >^{ V 8 j£< • . _ . _ _ : __ 


■a. •*[ =V^o«l ... ..._.. ._ , 


— — -^^§\iv ■ 


•3 - 




-2 




.1.1 , . _ _ 




1 _J 


29 io 1 -2 -3 4 -5 6 -7 -8 -9 00 .1 .2 -3 4 <5 -6 -7 -8 -9 



Fig. 83. 



In 1886, Professor \V. C. Unwin plotted logarithmically all the 
most trustworthy experiments on flow in pipes then available. 1 
Fig. 83 gives one such plotting. The results of measuring the slopes 
of the lines drawn through the plotted points are given in the 
table. 

It will be seen that the values of the index n range from 1-72 for 
the smoothest and cleanest surface, to 2-00 for the roughest. The 
numbers after the brackets are rounded off numbers. 

The value of n having been thus determined, values of mid" were 
next found and averaged for each pipe. These were again plotted 
logarithmically in order to find a value for x. The lines were not 
very regular, but in all cases the slope was greater than I to I, so 
that the value of x must be greater than unity. The following table 
gives the results and a comparison of the value of x and Reynolds's 
value 3-H. 



Kind of Pipe. 


n 


3-» 


■ 

X 


Tin plate .... 


1-72 


1-28 


I-IOO 


Wrought iron (Smith). 


i-75 


1-25 


I-2I0 


Asphalted pipes 


1-85 


115 


1-127 


i Wrought iron (Darcv) . 


1 -87 


i-i3 


l-68o 


Riveted wrought iron . 


1-87 


I-I3 


1-390 


Xew cast iron . 


i-95 


1-05 


1-168 


Cleaned cast iron 


2-00 


l-OO 


1-168 


ilncrusted cast iron 


2-00 


I'OO 


1 160 



Here, considering the great range of diameters and velocities in 
the experiments, the constancy of m is very satisfactorily close. 
The asphalted pipes give lather variable values. But, as some of 
these were new and some old, the variation is, perhaps, not surprising. 
The incrusted pipes give a value of m quite double that for new pipes 
but that is perfectly consistent with what is known of fluid friction 
in other cases. 



With the exception of the anomalous values for Darcy's wrought- 
iron pipes, there is no great discrepancy between the values of x and 
3-ra, but there is no appearance of relation in the two quantities. 
For the present it appears preferable to assume that x is independent 
of n. 

It is now possible to obtain values of the third constant m, using 
the values found for n and x. The following table gives the results, 
the values of m being for metric measures. 



Kind of Pipe. 



1 " Formulae for the Flow of Water in Pipes," Industries (Man- 
chester, 1886). 



Tin plate 
Wrought iron 



Asphalted 
pipes 



Riveted 

wrought iron 



New cast iron 

Cleaned cast 
iron 

Incrusted cast 
iron 



Diameter 

in 
Metres. 



Value of 



•01697"! 

•01676/ 

•01302 1 

■01319J 

•01749 

•02058 

•02107 

•01650 

•01317 

•02107 

•01370-1 

•01440 

•01390 y 
•01368 
■01 448 J 

•01725] 
•01427 1 
•01734 
•01745J 
■01979 
•02091 f- 
•01913J 
•03693 1 
•03530 y 
•03706 j 



Mean 
Value 
of m. 



Authority. 



•01686 
•01310 

•01831 • 

•01403 

•01658 

■01994 
03643 



Bossut 

Hamilton Smith 

Hamilton Smith 
W. W. Bonn 
W. W. Bonn 
Lampe 
Stearns 
Gale 

Hamilton Smith 



Darcy 

Darcy 
Darcy 



STEADY FLOW IN PIPES] 



HYDRAULICS 



63 



General Mean Values of Constants. 
The general formula (Hagen's) — hjl = mv n /d".2g — can therefore be 
taken to fit the results with convenient closeness, if the following 
mean values of the coefficients are taken, the unit being a metre : — 



Kind of Pipe. 


m 


X 


n 


Tin plate .... 


•0169 


I-IO 


1-72 


Wrought iron 


•0131 


I-2I 


i-75 


Asphalted iron . 


•0183 


I-I27 


1-85 


Riveted wrought iron . 


•0140 


I -390 


1-87 


New cast iron 


•0166 


I- 168 


1-95 


Cleaned cast iron 


•0199 


1-168 


2-0 


Incrusted cast iron 


•0364 


1-160 


2-0 



The variation of each of these coefficients is within a comparatively 
narrow range, and the selection of the proper coefficient for any given 
case presents no difficulty, if the character of the surface of the pipe 
is known. 

It only remains to give the values of these coefficients when the 
quantities are expressed in English feet. For English measures the 
following are the values of the coefficients : — 



Kind of Pipe. 


m 


X 


• ! 


Tin plate .... 


•0265 


I-IO 


1-72 


Wrought iron 


•0226 


I-2I 


i-75 


Asphalted iron . 


•0254 


1-127 


1-85 


Riveted wrought iron . 


■0260 


I -390 


1-87 


New cast iron . 


•0215 


1-168 


i-95 


Cleaned cast iron 


•0243 


I- 168 


2-0 


Incrusted cast iron 


•0440 


i- 160 


2-0 



§ 78. Distribution of Velocity in the Cross Section of a Pipe. — Darcy 
made experiments with a Pitot tube in 1850 on the velocity at 
different points in the cross section of a pipe. He deduced the 
relation 

V — » = ll'3(/3/R)V*\ 
where V is the velocity at the centre and v the velocity at radius r in 
a pipe of radius R with a hydraulic gradient i. Later Bazin repeated 
the experiments and extended them (Mem. de V Acadimie des Sciences, 
xxxii. No. 6). The most important result was the ratio of mean to 
central velocity. Let b = Ri/U 2 , where U is the mean velocity in the 
pipe; then V/U = 1 +9-03V6. A very useful result for practical 
purposes is that at 0-74 of the radius of the pipe the velocity is equal 
to the mean velocity. Fig. 84 gives the velocities at different radii 
as determined by Bazin. 

§ 79. Influence of Temperature on the Flow through Pipes. — Very 
careful experiments on the flow through a pipe 0-1236 ft. in diameter 



This shows a marked decrease of resistance as the temperature 
rises. If Professor Osborne Reynolds's equation is assumed 
h — niLV n /d i ~", and n is taken 1-795, then values of m at each 
temperature are practically constant — 

Temp. F. m. Temp. F. m. 

57 0-000276 100 0-000244 

70 0-000263 no 0-000235 

80 0-000257 120 0-000229 

90 0-000250 130 0-000225 

160 0-000206 

where again a regular decrease of the coefficient occurs as the 
temperature rises. In experiments on the friction of disks at 
different temperatures Professor W. C. Unwin found th-at the re- 
sistance was proportional to constant X (i-o-oo2i<) and the values 
of m given above are expressed almost exactly by the relation 
m =0-00031 1 (1-0-00215 /). 
In tank experiments on ship models for small ordinary variations 
of temperature, it is usual to allow a decrease of 3 % of resistance for 
io° F. increase of temperature. 

§ 80. Influence of Deposits in Pipes on the Discharge. Scraping 
Water Mains. — The influence of the condition of the surface of a pipe 
on the friction is shown by various facts known to the engineers of 
waterworks. Jn pipes which convey certain kinds of water, oxidation 
proceeds rapidly and the discharge is considerably diminished. A 
main laid at Torquay in 1858, 14 m. in length, consists of 10-in., 9-in. 
and 8-in. pipes. It was not protected from corrosion by any coating. 
But it was found to the surprise of the engineer that in eight years 
the discharge had diminished to 51 % of the original discharge. 
J. G. Appold suggested an apparatus for scraping the interior of the 
pipe, and this was constructed and used under the direction of 
William Froude (see " Incrustation of Iron Pipes," by W. Ingham, 
Proc. Inst. Mech. Eng., 1899). it was found that by scraping the 
interior of the pipe the discharge was increased 56%. The scraping 
requires to be repeated at intervals. After each scraping the dis- 
charge diminishes rather rapidly to 10% and afterwards more 
slowly, the diminution in a year being about 25 %. 

Fig. 85 shows a scraper for water mains, similar to Appold's but 
modified in details, as constructed by the Glenfield Company, at 
Kilmarnock. A is a longitudinal section of the pipe, showing the 
scraper in place; B is an end view of the plungers, and C, D sections 
of the boxes placed at intervals on the main for introducing or with- 
drawing the scraper. The apparatus consists of two plungers, 
packed with leather so as to fit the main pretty closely. On the 
spindle of these plungers are fixed eight steel scraping blades, with 
curved scraping edges fitting the surface of the main. The apparatus 
is placed in the main by removing the cover from one of the boxes 
shown at C, D. The cover is then replaced, water pressure is ad- 
mitted behind the plungers, and the apparatus driven through the 





Fig. 84. 

and 25 ft. long, with water at different temperatures, have been 
made by J. G. Mair (Proc. Inst. Civ. Eng. lxxxiv.). The loss of head 
was measured from a point 1 ft. from the inlet, so that the loss at 
entry was eliminated. The 15 in. pipe was made smooth inside and 
to gauge, by drawing a mandril through it. Plotting the results 
logarithmically, it was found that the resistance for all temperatures 
varied very exactly as » 1795 , the index being less than 2 as in 
other experiments with very smooth surfaces. Taking the ordinary 
equation of flow /j = f(4L/D)(» 2 /2g), then for heads varying from 1 ft. 
to nearly 4 ft., and velocities in the pipe varying from 4 ft. to 9 ft. per 
second, the values of f were as follows: — 



Temp. F. 


f 


Temp. F. 


f 


57 


•0044 to -0052 


100 


•0039 to -0042 


70 


•0042 to -0045 


no 


•0037 to -0041 


80 


•0041 to -0045 


120 


■0037 to -0041 


90 


•0040 to -0045 


130 


•0035 to -0039 






160 


•003-5 to -0038 



Fig. 85. Scale ^ 5 . 

main. At Lancaster after twice scraping the discharge was increased 
56!%, at Oswestry 545%. The increased discharge is due to the 
diminution of the friction of the pipe by removing the roughnesses 
due to oxidation. The scraper can be easily followed when the mains 
are about 3 ft. deep by the noise it makes. The average speed of the 
scraper at Torquay is 2\ rri. per hour. At Torquay 49 % of the 
deposit is iron rust, the rest being silica, lime and organic matter. 

In the opinion of some engineers it is inadvisable to use the 
scraper. The incrustation is only temporarily removed, and if the 
use of the scraper is continued the life of the pipe is reduced. The 
only treatment effective in preventing or retarding the incrustation 
due to corrosion is to coat the pipes when hot with a smooth and 
perfect layer of pitch. With certain waters such as those derived 
from the chalk the incrustation is of a different character, consisting 
of nearly pure calcium carbonate. A deposit of another character 
which has led to trouble in some mains is a black slime containing a 
good deal of iron not derived from the pipes. It appears to be an 



6 4 



HYDRAULICS 



[STEADY FLOW IN PIPES 



organic growth. Filtration of the water appears to prevent the 
growth of the slime, and its temporary removal may be effected by 
a kind of brush scraper devised by G. F. Deacon (see " Deposits in 
Pipes," by Professor J. C. Campbell Brown, Eroc. Inst. Civ. Eng., 
1 903- 1 904). 

§ 81. Flow of Water through Fire Hose. — The hose pipes used for 
fire purposes are of very varied character, and the roughness of the 
surface varies. Very careful experiments have been made by J. R. 
Freeman' (Am. Soc. Civ. Eng. xxi., 1889). It was noted that under 
pressure the diameter of the hose increased sufficiently to have a 
marked influence on the discharge. In reducing the results the true 
diameter has been taken. Let v = mean velocity in ft. per sec; 
r = hydraulic mean radius or one-fourth the diameter in feet; »' = 
hydraulic gradient. Then i> = »V (ri). 







Diameter 


Gallons 
(United 












Inches. 


States) 
per min. 


1 


V 


n 


Solid rubber 


\ 


2-65 


215 


•1863 


12-50 


i23'3 


hose 


,, 


344 


■4714 


20-00 


124-0 


Woven cotton, 


\ 


2-47 


200 


•2464 


13-40 


119-1 


rubber lined 


,, 


299 


•5269 


2O-00 


I2I-5 


Woven cotton, 


{ 


2-49 


200 


•2427 


13-20 


117-7 


rubber lined 


,, 


319 


•5708 


21 -OO 


122- 1 


Knit cotton, 


( 


2-68 


132 


•0809 


7-50 


III-6 


rubber lined 


( 


,, 


299 


•3931 


I7-00 


II4-8 


Knit cotton, 


( 


2-69 


204 


•2357 


11-50 


100- 1 


! rubber lined 


( 


,, 


319 


•5165 


18-00 


105-8 


Woven cotton , 


t 


2-12 


154 


•3448 


1.4-00 


"3-4 


rubber lined 


( 




240 


•7673 


2I-8I 


n8-4 


Woven cotton, 


\ 


2-53 


54-8 


•0261 


3-50 


94-3 


rubber lined 




298 


•8264 


19-00 


91-0 


Unlined linen 


{ 


2-60 


57-9 


•0414 


3-50 


73-9 


hose 


" 


33i 


1-1624 


20-00 


79-6 



§ 82. Reduction of a Long Pipe of Varying Diameter to an Equivalent 
Pipe of Uniform Diameter. Dupuit's Equation. — Water mains for 
the supply of towns often consist of a series of lengths, the diameter 
being the same for each length, but differing from length to length. 
In approximate calculations of the head lost in such mains, it is 
generally accurate enough to neglect the smaller losses of head 
and to have regard to the pipe friction only, and then the calcula- 
tions may be facilitated by reducing the main to a main of uniform 
diameter, in which there would be the same loss of head. Such a 
uniform main will be termed an equivalent main. 



— h- 



-U 



— 1$ - 



1 



"W 



B 



Fig. 86. 



§ 83. Other Losses of Head in Pipes. — Most of the losses of head in 
pipes, other than that due to surface friction against the pipe, are due 
to abrupt changes in the velocity of the stream producing eddies. 
The kinetic energy of these is deducted from the general energy of 
translation, and practically wasted. 

Sudden Enlargement of Section. — Suppose a pipe enlarges in section 
from an area too to an area «i (fig. 
87); then II 

fli/vo •= «o/ wi ; i^^HH^MaJI 

or, if the section is circular, 
»iM> = (do/'di) 2 . 

The head lost at the abrupt change 

of velocity has already been wm 
shown to be the head due to the 
relative velocity of the two parts 
of the stream. Hence head lost 



In fig. 86 let A be the main of variable diameter, and B the equiva- 
lent uniform main. In the given main of variable diameter A, let 
h, h... be the lengths, 
di, di... the diameters, 
»i, »2... the velocities, 
ii, ii... the slopes, 
for the successive portions, and let I, d, v and i be corresponding 
quantities for the equivalent uniform main B. The total loss of 
head in A due to friction is 

h = i 1 l 1 -\-i 2 l 2 -\- . . . 
= f W-4il2&di) + f W-<\kl2ga\) + ... 
and in the uniform main 

il = ?(fl 2 - 4l/2gd). 
If the mains are equivalent, as defined above, 

f(y-4//2g<f) = f (^• 4 / 1 /2grf 1 ) -t-fW-4fc/2gd2) + • - . 
But, since the discharge is the same for all portions, 

\tt(Pv = jxii 2 f 1 = jfttj = . . . 
Vi = vd l jd? ; !> 2 = vtPjcL? . . . 

Also suppose that f may be treated as constant for all the pipes. 
Then 

lid = (rfVdi 4 ) (hid,) + (dW) (hid*) + ... 
l=(d°jd l >)h + (d i /d 2 °)h+... 
which gives the length of the equivalent uniform main which would 
have the same total loss of head for any given discharge. 



V. 



Fig. 87. 



h = (l'»-ViYl2g = (W"0 - I ) V/2g = { (djdtf- 
Or fi e = £eVl*/2g, 

if f,. is put for the expression in brackets. 



■i}V/2g 



(1) 



ui/uo = 


1.1 


1.2 


1-5 


1-7 


1.8 


1-9 


2.0 


2-5 


30 


3-5 


4-0 


5-0 


6.0 


7.0 


S.o 


di/do = 


1.05 


1. 10 


1.22 


1.30 


1-34 


1.38 


1.41 


1.58 


1-73 


1.87 


2.00 


2.24 


2.45 


2.65 


2.83 


f.= 


.01 


.04 


•25 


•49 


.64 


.81 


1. 00 


2.25 


4.00 


6.2s 


9.00 


16.00 


25-00 


36.0 


49-0 



Abrupt Contraction of Section. — When water passes from a larger 
to a smaller section, as in figs. 88, 89, a contraction is formed, and 
the contracted stream abruptly expands to fill the section of the pipe. 





Fig. 



Fig. 



Let &> be the section and v the velocity of the stream at bb. At aa 
the section will be c c a, and the velocity (io/ccu)v = v/ci, where c c is 
the coefficient of contraction. Then the head lost is 

T)m = (vlc c -vy/2g=(i/c c -i)V/2g; 

and, if c c is taken 0-64, 

| m = o-3i6i- 2 /2g. (2) 

The value of the coefficient of contraction for this case is, however, 
not well ascertained, and the result is somewhat modified by friction. 
For water entering a cylindrical, not bell-mouthed, pipe from a 
reservoir of indefinitely large size, experiment gives 

§.. = 0-505 vy 2 g. (3) 

If there is a diaphragm at the mouth of the pipe as in fig. 89, let wi 
be the area of this orifice. Then the area of the contracted stream 
is c C ">i, and the head lost is 

h c = !(a)/CcWi)-llV/2g 

= f^/2g (4) 

if f, is put for { (w/c c o>i) — I ) 2 . Weisbach has found experimentally 
the following values of the coefficient, when the stream approaching 
the orifice was considerably larger than the orifice : — 



OJl/W = 


0.1 


0.2 


0-3 


0.4 


0-5 


0.6 


0.7 


0.8 


0.9 


1.0 


C c = 


.616 


.614 


.612 


.610 


.617 


.605 


.603 


.601 


■598 


•596 


f.= 


231-7 


5°-99 


19.78 


9.612 


5-256 


3-077 


1.876 


1 169 


0-734 


0.480 



When a diaphragm was placed in a tube of uniform section (fig. 90) 



JL 



Fig. 90. 

the following values were obtained, ui being the area of the orifice 
and w that of the pipe: — 



t*)i/co = 


O.I 


0.2 


0.3 


O.A 


OS 


0.6 


0.7 


0.8 


0.0 


1.0 


Ce = 


.624 


.632 


.643 


•659 


.68: 


.712 


• 755 


.813 


.892 


1 .00 


*« = 


225.9 


47-77 


30.83 


7.801 


1.753 


1.796 


• 797 


.290 


.060 


.000 



STEADY FLOW IN PIPES] 



HYDRAULICS 



65 



Elbows. — Weisbach considers the loss of head at elbows (fig.91) 
to be due to a contraction formed by the stream. From experiments 
with a pipe 1 { in. diameter, he found the loss of head 

fi« = f^/2g; (5) 

fe =0-9457 sin 2 j0+2-o47 sin 4 \$. 



= 


20° 
O.O46 


40° 
0.130 


60° 
0.364 


80° 
0.740 


90 

O.984 


I0O° 

1.260 


IIO° 

1.556 


120° 
1. 861 


I30° 
2.IS8 


I40 
2.431 



Hence at a right-angled elbow the whole head due to the velocity 

very nearly is lost. 

Bends. — Weisbach traces the loss of head at curved bends to a 

similar cause to that at 
elbows, but the coeffi- 
cients for bends are not 
very satisfactorily ascer- 
tained. Weisbach ob- 
tained for the loss of 
head at a bend in a pipe 
of circular section 

^ = fi,f 2 /2g; (6) 

ft =0-131 +i-847(d/2p)S, 

where d is the diameter 

V of the pipe and p the 

Fig. 91. radius of curvature of 

the bend. The resistance 

at bends is small and at present very ill determined. 

Valves, Cocks and Sluices. — These produce a contraction of the 
water-stream, similar to that for an abrupt 
diminution of section already discussed. The 
loss of head may be taken as before to be 

$» = f,»72g; (7) 

where v is the velocity in the pipe beyond the valve 
and f„ a coefficient determined by experiment. The 
following are Weisbach's results. 

Sluice in Pipe of Rectangular Section (fig. 92). 
Section at sluice =wi in pipe=co. 




Fig. 92. 



1 f - 


1-0 
0-00 


0-9 
•09 


o-8 
•39 


0-7 
•95 


o-6 
2-08 


o-5 
4-02 


0-4 

8-12 


o-3 

17-8 


0-2 

44-5 


O-I 

193 



Sluice in Cylindrical Pipe (fig. 93). 



Ratio of height oft 


















opening to diameter > 


1.0 


4 


i 


* 


* 


if 


} 


i 


of pipe ] 


















wi/co — 


1. 00 


0.948 


.856 


.740 


.609 


.466 


■315 


• 159 


f.= 


0.00 


0.07 


0.26 


0.81 


2.06 


552 


17.0 


07.8 





Fig. 93. 



Fig. 94. 



Cock in a Cylindrical Pipe (fig. 94). Angle through which cock 
is turned =0. 



8 = 


5° 


10° 


15° 


20° 


25° 


30° 


35° 


Ratio of"j 
















cross :- 
sections J 


•926 


•850 


•772 


•692 


■613 


•535 


•458 
















f > = 


■05 


•29 


•75 


1-56 


3-10 


5-47 


9-68 



8 = 
Ratio of 
cross 
sections 

f- = 



40" 
•385 
17-3 



45° 
•315 
31-2 



J 55 



•250 
526 



•190 
10G 



60° 
•137 

2"6 



65° 
•091 
486 



82° 

o 

00 



Throttle Valve in a Cylindrical Pipe (fig. 95) 



" 


















= 


_ 



10° 


15° 


20° 


25° 


30* 


35° 


40° 


f» = 


•24 


•52 


•90 


i-54 


2-51 


3-91 


6-22 


io-8 



= 

r.= 


45° 
i8- 7 


5o° 
32-6 


55° 
58-8 


60 ° 
118 


65° 
256 


70° 
751 


90° 

00 



M\'fi'-l'«^ 





„i 



§ 84. Practical Calculations on the Flow of Water in Pipes. — In 
the following explanations it will be assumed that the pipe is of so 
great a length that only the 

loss of head in friction against ..-'' 

the surface of the pipe needs 
to be considered. In general 
it is one of the four quantities 
d, i, v or Q which requires 
to be determined. For since 
the loss of head h is given by 
the relation h = il, this need 
not be separately considered. 

There are then three equa 
tions (see eq. 4, 
as arise : — 

f = o(i + i/i2d); 
where 0=0-005 for new and=o-oi for incrusted pipes. 
f» 2 /2g = \di. 
Q = l-xdh). 



w///,w/w/#. // 



Y'f/?0/////tf///ttS//{//////M} t 



Fig. 95. 
72, and 9a, § 76) for the solution of such problems 

(1) 



(2) 
(3) 



Problem 1. Given the diameter of the pipe and its virtual slope, 
to find the discharge and velocity of flow. Here d and i are given, 
and Q and v are required. Find f from (1) ; then v from (2) ; lastly 
Q from (3). This case presents no difficulty. 

By combining equations (1) and (2), v is obtained directly: — 

!> = V(g<K/2f)=V(g/2a)V [<«/{! +I/I2d} ]. (4) 

For new pipes . . V (g/2a) =56-72 

For incrusted pipes . =40-13 

For pipes not less than 1, or more than 4 ft. in diameter, the 
mean values of f are 

For new pipes 0-00526 

For incrusted pipes 0-01052. 

Using these values we get the very simple expressions — 

i> = 55-3iV (di) for new pipes £ (4a) 

= 39-1 1 V (di) for incrusted pipes 5 ' 
Within the limits stated, these are accurate enough for practical 
purposes, especially as the precise value of the coefficient \ cannot 
be known for each special case. 

Problem 2. Given the diameter of a pipe and the velocity of flow, 
to find the virtual slope and discharge. The discharge is given by 
(3); the proper value of f by (1); and the virtual slope by (2). 
This also presents no special difficulty. 

Problem 3. Given the diameter of the pipe and the discharge, to 
find the virtual slope and velocity. Find v from (3); f from (1); 
lastly i from (2). If we combine (1) and (2) we get 

* = f(W2g) (4/d)=2a{i + i/i2dy/gd; (5) 

and, taking the mean values of f for pipes from 1 to 4 ft. diameter, 
given above, the approximate formulae are 

1 = 0-0003268 v 2 /d for new pipes \ (5a) 

= 0-0006536 v*/d for incrusted pipes ) " 
Problem 4. Given the virtual slope and the velocity, to find the 
diameter of the pipe and the discharge. The diameter is obtained 
from equations (2) and (1), which give the quadratic expression 
d i — d(2av 2 jgi) — av 2 /6gi = o . 
.■.d = avygi+ij{( a v l 'lgi) (a.vVgi+l/6)}. (6). 

For practical purposes, the approximate equations 

d = 2av i lgi + ili2 (6a) 

= 0-00031 v 2 /i+-o83 for new pipes 
= 0-00062 ti 2 /i+-o83 for incrusted pipes 
are sufficiently accurate. 

Problem 5. Given the virtual slope and the discharge, to find the 
diameter of the pipe and velocity of flow. This case, which often 
occurs in designing, is the one which is least easy of direct solution. 
From equations (2) and (3) we get— 

<2 B = 32fQ7g*- 2 *'- (7) 

If now the value of f in (1) is introduced, the equation becomes very 
cumbrous. Various approximate methods of meeting the difficulty 
may be used. 

(a) Taking the mean values of f given above for pipes of 1 to 4 
ft. diameter we get 

<Z = V(32f/gT 2 )V(Q. 2 A') (8) 

= 0-22 16 V (Q 2 /i) for new pipes 
= 0-2541 V (Q 2 /*) for incrusted pipes; 

equations which are interesting as showing that when the value of 
f is doubled the diameter of pipe for a given discharge is only in- 
creased by 13%. 



66 



HYDRAULICS 



[STEADY FLOW IN PIPES 



(b) A second method is to obtain a rough value of d by assuming 
f = a. This value is 

d' = V (32QVgT'i) V a =06319 V (Q7»')V a. 

Then a very approximate value of f is 

f' = o(l + i/i2d'); 
and a revised value of d, not sensibly differing from the exact value, 
is 

d" = V (32Q 2 , g* 2 i) V f =0-6319 V (Q7»)V r'. 

(c) Equation 7 may be put in the 
form 

d = V (32aQ 2 /gx^)V (I +ljI2d). (9) 

Expanding the term in brackets, 

K l (i+ili2d)=i+i,'6od-ili8ood i ... 

Xeglectingthetermsafterthesecond, 

d = ^(32<i/g7r J )V(Q 2 /i)-!i+i/6od! 

= V (32a/g7r 2 )V (Q 2 /*) +o-oi667;( 9 o) 
and 
V(32a/g7r 2 ) =0-219 for new pipes 

= 0-252 f or incrusted pipes. 

§ 85. Arrangement of Water Mains i 

/or Towns' Supply. — Town mains are J'- 

usually supplied oy gravitation from 
a service reservoir, which in turn is 

supplied by gravitation from a storage reservoir or by pumping 
from a lower level. The service reservoir should contain three 
days' supply or in important cases much more. Its elevation 
should be such that water is delivered at a pressure of at least about 
100 ft. to the highest parts of the district. The greatest pressure in 
the mains is usually about 200 ft., the pressure for which ordinary 
pipes and fittings are designed. Hence if the district supplied has 



if the average demand is 25 gallons per head per day, the mains 
should be calculated for 50 gallons per head per day. 

§ 86. Determination of the Diameters of Different Parts of a Water 
Main. — When the plan of the arrangement of mains is determined 
upon, and the supply to each locality and the pressure required is 
ascertained, it remains to determine the diameters of the pipes. Let 
fig. 97 show an elevation of a main ABCD . . . , R being the reservoir 
from which the supply is derived. Let NN be the datum line of the 
levelling operations, and H„, Hi... the heights of the main above 
the datum line, H r being the height of the water surface in the 





Fig. 96. 

great variations of level it must be divided into zones of higher and 
lower pressure. Fig. 96 shows a district of two zones each with its 
service reservoir and a range of pressure in the lower district from 
100 to 200 ft. The total supply required is in England about 25 
gallons per head per day. But in many towns, and especially in 
America, the supply is considerably greater, but also in many cases 




'*N " 



....hrr^?." 'i^;A^:.'::i:^:::::r:f?.\7:i;":.t.i. 

Fig. 97. 



a good deal of the supply is lost by leakage of the mains. The supply 
through the branch mains of a distributing system is calculated from 
the population supplied. But in determining the capacity of the 
mains the fluctuation of the demand must be allowed for. It is usual 
to take tfee saaximum demand at twice the average demand. Hence 



reservoir from the same datum. Set up next heights AAl, BBi, . . . 
representing the minimum pressure height necessary for the adequate 
supply of each locality. Then A1B1OD1 ... is a line which should 
form a lower limit to the line of virtual slope. Then if heights 
&<., t)b, fyc... are taken representing the actual losses of head in each 
length U, h, h— of the main, AoB Co will be the line of virtual 
slope, and it will be obvious at what points such as Do and E , the 
pressure is deficient, and a different choice of diameter of main is 
required. For any point z in the length of the main, we have 
< Pressure height = H r -H i -(B„+B f ,+ . . .6,). 
Where no other circumstance limits the loss of head to be assigned 
to a given length of main, a consideration of the safety of the main 
from fracture by hydraulic shock leads to a limitation of the velocity 
of flow. Generally the velocity in water mains lies between I J and 
4! ft. per second. Occasionally the velocity in pipes reaches 10 ft. 
per second, and in hydraulic machinery working under enormous 
pressures even 20 ft. per second. Usually the velocity diminishes 
along the main as the discharge diminishes, so as to reduce somewhat 
the total loss of head which is liable to render the pressure insufficient 
at the end of the main. 

J. T. Fanning gives the following velocities as suitable in pipes 
for towns' supply : — 

Diameter in inches . 4 8 12 18 24 30 36 

Velocity in feet per sec. . 2-5 3-0 3-5 4-5 5-3 6-2 7-0 

§ 87. Branched Pipe connecting Reservoirs at Different Levels. — Let 
A, B, C (fig. 98) be three reservoirs connected by the arrangement of 
pipes shown, — h, di, Qi, »i; h, d 2 , Q 2 , Vi\ h, d 3 , Q 3 , v 3 being the 
length, diameter, discharge and velocity in the three portions of 
the main pipe. Suppose the dimensions and positions of the pipes 
known and the discharges required. 

If a pressure column is introduced at X, the water will rise to a 
height XR, measuring the pressure at X, and aR, R6, Re will be the 
lines of virtual slope. If the free surface level at R is above b, the 

reservoir A supplies B and C, and if 
R is below b, A and B supply C. 
Consequently there are three cases : — 

I. R above i;Qi=Q 2 +Q 3 . 
II. R level with b; Qi = Q 3 ; Q 2 =0 
III. R below ft^+Q^Q,. 
To determine which case has to be 
dealt with in the given conditions, 
suppose the pipe from X to B closed 
by a sluice. Then there is a simple 
main, and the height of free surface 
¥ at X can be determined. For this 
condition 

h a -h' = f (i>i 2 /2g) (^lifdi) 

= 32fQ' 2 />/g*- 2 d l 5 ; 
h'-h c = i{v^l2g){4zld,) 

=32fQ%fer 2 d3 5 ; 
where Q' is the common discharge 
of the two portions of the pipe. 
Hence 

(/i„-/0/(/i'-W=W3 5 /Wi 5 , 

from which h' is easily obtained. If then V is greater than hb. 
opening the sluice between X and B will allow flow towards B, and 
the case in hand is case I. If h' is less than h b , opening the sluice 
will allow flow from B, and the case is case III. If h' = h b , the case 
is case II., and is already completely solved. 



ar 



COMPRESSIBLE FLUIDS IN PIPES] 



HYDRAULICS 



67 



The true value of h must lie between V and lib- Choose a new 
value of h, and recalculate Qi, Q 2 , Q 3 . Then if 

Qi>Qi+Qs in case I., 
or 0i+Q2>Qa in case III., 

the value chosen for h is too small, and a new value must be chosen. 

If 

Qi<Q2+Q 3 incase I., 
or Qi+y 2 <Q 3 in case III., 

the value of h is too great. 

Since the limits between which h can vary are in practical cases not 
very distant, it is easy to approximate to values sufficiently accurate. 

§ 88. Water Hammer. — If in a pipe through which water is flowing 
a sluice is suddenly closed so as to arrest the forward movement of 
the water, there is a rise of pressure which in some cases is serious 
enough to burst the pipe. This action is termed water hammer or 
water ram. The fluctuation of pressure is an oscillating one and 
gradually dies out. Care is usually taken that sluices should only be 
closed gradually and then the effect is inappreciable. Very careful 
experiments on water hammer were made by N. J. joukowsky at 
Moscow in 1898 (Stoss in Wasserleilungen, St Petersburg, 1900), and 
the results are generally confirmed by experiments made by E. B. 
Weston and R. C. Carpenter in America. Joukowsky used pipes, 
2, 4 and 6 in. diameter, from 1000 to 2500 ft. in length. The sluice 
closed in 0-03 second, and the fluctuations of pressure were auto- 
matically registered. The maximum excess pressure due to water- 
hammer action was as follows : — 



Pipe 4-in. diameter. 


Pipe 6-in. diameter. 


Velocity 
ft. per sec. 


Excess Pressure, 
lb per sq. in. 


Velocity 
ft. per sec. 


Excess Pressure, 
lb per sq. in. 


o-5 
2-9 

41 


31 
168 
232 
519 


0-6 
3-0 
5-6 

7-5 


43 
173 
369 
426 



In some cases, in fixing the thickness of water mains, 100 lb per sq. in. 
excess pressure is allowed to cover the effect of water hammer. 
With the velocities usual in water mains, especially as no valves can 
be quite suddenly closed, this appears to be a reasonable allowance 
(see also Carpenter, Am. Soc. Mech. Eng., 1893). 

IX. FLOW OF COMPRESSIBLE FLUIDS IN PIPES 
§ 89. Flow of A ir in Long Pipes. — When air flows through a long 
pipe, by far the greater part of the work expended is used in over- 
coming frictional resistances due to the surface of the pipe. The 
work expended in friction generates heat, which for the most part 
must be developed in and given back to the air. Some heat may 
be transmitted through the sides of the pipe to surrounding materials, 
but in experiments hitherto made the amount so conducted away 
appears to be very small, and if no heat is transmitted the air in the 
tube must remain sensibly at the same temperature during expansion. 
In other words, the expansion may be regarded as isothermal 
expansion, the heat generated by friction exactly neutralizing the 
cooling due to the work done. Experiments on the pneumatic tubes 
used for the transmission of messages, by R. S. Culley and R. Sabine 
(Proc. Inst. Civ. Eng. xliii.), show that the change of temperature of 
the air flowing along the tube is much less than it would be in adia- 
batic expansion. 

§ 90. Differential Equation of the Steady Motion of Air Flowing in 
a Long Pipe of Uniform Section. — When air expands at a constant 
absolute temperature r, the relation between the pressure p in 
pounds per square foot and the density or weight per cubic foot G 
is given by the equation 

P!G=ct, (1) 

where £=53-15. Taking 7 = 521, corresponding to a temperature of 
60° Fahr., 

ct = 27690 foot-pounds. (2) 

The equation of continuity, which expresses the condition that in 
steady motion the same weight of fluid, W, must pass through each 

cross section of the stream in 

BBBoHBBSBBBBBBBBEmB, the unit of time, is 

1 i ; ; Gf2w = W = constant, (3) 

where SI is the section of the 
pipe and u the velocity of 
the air. Combining (1) and 

(3). 

Slup/W =cr = constant. (3a) 

Since the work done by 

gravity on the air during its 

flow through a pipe due to 






A Q 



A'o 



■&i 



Aj 



Fig. 99. 



time dt the mass of air between A0A1 comes to A'oA'i so that A A'o = 
udt and AiA'j = {u-\rdu)dti. Let il be the section, and m the hydraulic 
mean radius of the pipe, and W the weight of air flowing through the 
pipe per second. 

From the steadiness of the motion the weight of air between the 
sections AoA'o, and AiA'i is the same. That is, 
\\ 1 dt = GSludt = GQ(u+du)dt. 
By analogy with liquids the head lost in friction is, for the length 
dl (see § 72, eq. 3), £(u 2 /2g)(dl/m). Let H=« 2 /2g. Then the head 
lost is f(H/j»)a7; and, since Wd/ lb of air flow through the 
pipe in the time considered, ^he work expended in friction is 
— f(H/«)Wtf7 dt. The change of kinetic energy in dt seconds is the 
difference of the kinetic energy of AoA'o and AiA\, that is, 
(W/g)dt\ (u+du) 2 - w 2 !/2 = (W/g) u du dt = W'dHd t. 
The work of -expansion when Qttdt cub. ft. of air at a pressure 
p expand to il(u-\-du)dt cub. ft. is Qpdudt. But from (3a) 
u = CT\V/ap, and therefore 

duldp^-crVvjilpK 
And the work done by expansion is— (crW lp)dp dt. 

The work done by gravity on the mass between Ao and Ai is zero 
if the pipe is horizontal, and may in other cases be neglected without 
great error. The work of the pressures at the sections A0A1 is 
pnudt— (p+dp)Q(u+du)dt 
= ~(pdu+udp)Odt 
But from (3a) 

pu = constant, 
pdu+udp — o, 
and the work of the pressures is zero. Adding together the quantities 
of work, and equating them to the change of kinetic energy. 
WdUdt = - {cTVJIp)dpdt-^{H/m)\\dldt 
dH + (cr/p)dp + t;(Hlm)dl = o, 
dH/H + (crlHp)dp+^dl/m = o (4) 

But v = CTWXtp, 

and H=w 2 /2g = cV 2 W 2 /2,?Q 2 £ 2 , 

.'. dll/H + (2gil i p/crW 2 )dp + t:dllm = o. (4a) 

For tubes of uniform section m is constant ; for steady motion W 
is constant ; and for isothermal expansion 7- is constant. Integrating, 

log H-f-gfi 2 £ 2 /W 2 cr+f//« = constant; (5) 

for l = o, let H = H , and p = pt>; 

and for / = /, let H = Hi, and p — pi. 

log (Hi/Ho) + (gfiVWVr) (p? - pj) + Him = o. (5a) 

where pa is the greater pressure and pi the less, and the flow is from 
Ao towards Ai. 

By replacing W and H, 

log(pt>/p 1 ) + (gcTi'uti i p<?)(pi 1 — p(i') + ?l/m =0. 
Hence the initial velocity in the pipe is 

«o = V [{sCTW-pSMPoKil/m+logfalpO}]. 
When / is great, log palpi is comparatively small, and then 

«o = V[(gcrw/f/){(^-/. 1 »)/^)], 
a very simple and easily used expression. For pipes 
section m=d/4, where d is the diameter: — 

«o = V [(gCTdltflMPo'-pftlp**}] ; 
or approximately 

Wo = (i ■ 1319 — 0-J264pi/po)\' (gcrd/tfl). 

§ 91. Coefficient of Friction for Air. — A discussion by 
Unwin of the experiments by Culley and Sabine on the rate of 
transmission of light carriers through pneumatic tubes, in which 
there is steady flow of air not sensibly affected by any resistances 
other than surface friction, furnished the value f =-007. The pipes 
were lead pipes, slightly moist, 2f in. (0-187 ft-) m diameter, and in 
lengths of 2000 to nearly 6000 ft. 

In some experiments on the flow of air through cast-iron pipes 
A. Arson found the coefficient of friction to vary with the velocity and 
diameter of the pipe. Putting 

r=«A'+/3, (8) 

he obtained the following values — 



variations of its level is generally small compared with the work 
done by changes of pressure, the former may in many cases be 
neglected. 

Consider a short length dl of the pipe limited by sections Ao, Ai at 
a distance dl (fig. 99). Let p, u be the pressure and velocity at Ao, 
p+dp and u+du those at Ai. Further, suppose that in a very short 



(6) 

(7) 



(7a) 
of circular 

(7b) 

(7f) 
Professor 



Diameter of Pipe 




P 


f for 100 ft. j 


in feet. 




per second. 


1-64 


•00129 


•00483 


•00484 


1-07 


■00972 


•00640 


•00650 


•83 


•01525 


•00704 


•00719 . 


■338 


•03604 


■00941 


■00977 


•266 


•03790 


■00959 


•00997 


•164 


•04518 


•01 167 


•01212 J 



It is worth while to try if these numbers can be expressed in the 
form proposed by Darcy for water. For a velocity of 100 ft. per 
second, and without much enor for higher velocities, these numbers 
agree fairly with the formula 

c = 0-005(1 +3/10J), (q) 

which only differs from Darcy's value for water in that the second 
term, which is always small except for very small pipes, is larger. 



68 



HYDRAULICS 



[FLOW IN RIVERS 



Some later experiments on a very large scale, by E. Stockalper 
at the St Gotthard Tunnel, agree better with the value 
f = 0-0028(1 +3/iod). 

These pipes were probably less rough than Arson's. 

When the variation of pressure is very small, it is no longer safe 
to neglect the variation of level of the pipe. For that case we may 
neglect the work done by expansion, and then 

zo-2i-po/Go-£i/Gi-r(»V22) (JIm)=o, (10) 

precisely equivalent to the equation for the flow of water, So and Zi 
being the elevations of the two ends of the pipe above any datum, 
ft and ft the pressures, Go and Gi the densities, and v the mean 
velocity in the pipe. This equation may be used for the flow of 
coal gas. 

§ 92. Distribution of Pressure in a Pipe in which Air is Flowing. — 
From equation (7a) it results that the pressure p, at / ft. from that 
end of the pipe where the pressure is po, is 

p = ft V { 1 - iWlmgcr j ; (11) 

which is of the form 

p = TJ(al+b) 
for any given pipe with given end pressures. The curve of free sur- 
face level for the pipe is, therefore, a parabola with horizontal axis. 
Fig. 100 shows calculated curves of pressure for two of Sabine's 
experiments, in one of which the pressure was greater than atmo- 




;1S75 



2113-SFt. 



4-2 27 Ft. 

Fig. 100. 



eaio-JtF*- 



s*s*Ft, 



spheric pressure, and in the other less than atmospheric pressure. 
The observed pressures are given in brackets and the calculated 
pressures without brackets. The pipe was the pneumatic tube be- 
tween Fenchurch Street and the Central Station, 2818 yds. in length. 
The pressures are given in inches of mercury. 

Variation of Velocity in the Pipe. — Let pa, Uo be the pressure 
and velocity at a given section ot the pipe; p, u, the pressure and 
velocity at any other section. From equation (3a) 

up = ci-WVn = constant ; 
so that, for any given uniform pipe, 

Up=U($pt>, 

u = u po!p; (12) 

which gives the velocity at any section in terms of the pressure, 
which has already been determined. Fig. 101 gives the velocity 









,_^---Hr*55*^^^-£ 






Vo*" 1 "^— — - 








■ Pr*asur* — . 


_- —yrvl ' 




— — — "jfe*"** — 


_ — -~Y2*- fl 






?22' a 


1 




T»* 




1 
1 

1 
1 
1 

I 







21I.i-.SH. 


+2 27 n. 


634-oatt. 04-54 



than to telegraph by electricity. The tubes are laid underground 
with easy curves; the messages are made into a roll and placed in 
a light felt carrier, the resistance of which in the tubes in Lor.don 
is only J oz. A current of air forced into the tube or drawn through 
it propels the carrier. In most systems the current of air is steady 
and continuous, and the carriers are introduced or removed without 
materially altering the flow of air. 

Time of Transit through the Tube. — Putting t for the time of transit 
from o to /, 

t= I dl/u, 
1 

From (40) neglecting rfH/H, and putting m=dja r% 
dl = gdSPpdpfciW'-cr. 



From (1) and (3) 



Fig. ioi. 

curves for the two experiments of Culley and Sabine, for which the 
pressure curves have already been drawn. It will be seen that the 
velocity increases considerably towards that end of the pipe where 
the pressure is least. 

§ 93. 'Weight of Air Flowing per Second. — The weight of air dis- 
charged per second is (equation 30) — 

W = S2woft/ci-. 
From equation (76), for a pipe of circular section and diameter d, 
W = iH kdHpf-pVlrlcT), 

= -6nVi<2 5 (A> 2 -£iWr|. (13) 

Approximately 

W = (-6916ft- -4438ft) (d b l^r)i. (13a) 

§ 94. A pplication to the Case cf Pneumatic Tubes for the Trans- 
mission of Messages. — In Paris, Berlin, London, and other towns, it 
has been found cheaper to transmit messages in pneumatic tubes 



w = Wc-r/ft2; 
dlju =gda 3 p-dp/2^WVT- ; 



/ = 



( ^gda 3 pHpl2tw s c 2 T\ 

= g<ta 3 (ft 3 -ft 3 )/6fW 3 cV. 
But W = ftz<ofl/cr; 

.-. t =gdcr(ft 3 -ft 3 )/6rft 3 «o 3 , 

= firs(ft^ft 3 )/6(gcrrf)i(ft 2 -ft 2 )?- 
If r = 52i°, corresponding to 60° F., 

/ = -ooi4i2r^(ft 3 -ft 3 )/iKft 2 -ft 2 )5; 
which gives the time of transmission in terms of the initial and final 
pressures and the dimensions of the tube. 

Mean Velocity of Transmission. — The mean velocity is Ijt; or, for 
t = 52i°, 

2*mean=0-708V{<Z(ft 2 -ft 2 )2/#(A 3 -ft 3 )!- (l6) 

The following table gives some results :— 



(14) 



(15) 
(15a) 





Absolute 
Pressures in 
ft per sq. in. 


Mean Velocities for Tubes of a 
length in feet. 




po 


ft 


1000 


2000 


3000 


4000 


5000 


Vacuum ( . 
Working / . 

Pressure 1 ' 
Working 1 ' 


15 
15 
20 

25 
30 


5 
10 

15 
15 
15 


99-4 
67-2 
57-2 
74-6 
84-7 


70-3 
47-5 
40-5 
52-7 
6o-o 


57-4 
38-8 
33-0 
43-i 
49..0 


497 

34-4 
28-6 

37-3 
42-4 


44-5 
30-1 
25-6 
33-3 
37-9 



Limiting Velocity in the Pipe when the Pressure at one End is 
diminished indefinitely. — If in the last equation there be put ft=o, 
then 

tt' mean = o-7o8V WfO; 
where the velocity is independent of the pressure ft at the other 
end, a result which apparently must be absurd. Probably for long 
pipes, as for orifices, there is a limit to the ratio of the initial and 
terminal pressures for which the formula is applicable. 

X. FLOW IN RIVERS AND CANALS 

§ 95. Flow of Water in Open Canals and Rivers. — When water 
flows in a pipe the section at any point is determined by the form 
of the boundary. When it flows in an open channel with free upper 
surface, the section depends on the velocity due to the dynamical 
conditions. 

Suppose water admitted to an unfilled canal. The channel will 
gradually fill, the section and velocity at each point gradually 
changing. But if the inflow to the canal at its head is constant, 
the increase of cross section and diminution of velocity at each 
point attain after a time a limit. Thenceforward the section and 
velocity at each point are constant, and the motion is steady, or 
permanent regime is established. 

If when the motion is steady the sections of the stream are all 
equal, the motion is uniform. By hypothesis, the inflow Qv is con- 
stant for all sections, andfl is constant; therefore v must be constant 
also from section to section. The case is then one of uniform steady 
motion. In most artificial channels the form of section is constant, 
and the bed has a uniform slope. In that case the motion is uniform, 
the depth is constant, and the stream surface is parallel to the bed. 
If when steady motion is established the sections are unequal, the 
motion is steady motion with varying velocity from section to 
section. Ordinary rivers are in this condition, especially where the 
flow is modified by weirs or obstructions. Short unobstructed 
lengths of a river may be treated as of uniform section without great 
error, the mean section in the length being put for the actual sections. 

In all actual streams the different fluid filaments have different 
velocities, those near the surface and centre moving faster than 
those near the bottom and sides. The ordinary formulae for the 
flow of streams rest on a hypothesis that this variation of velocity 
may be neglected, and that all the filaments may be treated as having 
a common velocity equal to the mean velocity of the stream. On 
this hypothesis, a plane layer abab (fig. 102) between sections normal 



AND CANALS] 



HYDRAULICS 



6 9 



to the direction of motion is treated as sliding down the channel to 
a'a'b'V without deformation. The component of the weight parallel 
to the channel bed balances the friction against the channel, and 
in estimating the friction the velocity of rubbing is taken to be the 
mean velocity of the stream. In actual streams, however, the 
velocity of rubbing on which the friction depends is not the mean 



variation of the coefficient of friction with the velocity, proposed an 
expression of the form 

f = a(l+/3/D), (5) 

and from 255 experiments obtained for the constants the values 

a = 0-0O7409; (3 = 0-1920. 

This gives the following values at different velocities: — 



v = 


o-3 
0-01215 


o-5 
0-01025 


0-7 
0-00944 


1 

0-00883 


0-00836 


2 

0-00812 


3 
0-90788 


5 
0-00769 


7 
0-00761 


10 
0-00755 


15 
0-00750 




velocity of the stream, and is not in any simple relation with it, for 

channels of different forms. The 
theory is therefore obviously based 
on an imperfect hypothesis. How- 
ever, by taking variable values for 
the coefficient of friction, the errors 
of the ordinary formulae are to a 
great extent neutralized, and they 
may be used without leading to 
practical errors. Formulae have 
been obtained based on less re- 
stricted hypotheses, but at present they are not practically so 
reliable, and are more complicated than the formulae obtained in 
the manner described above. 

§ 96. Steady Flow of Water with Uniform Velocity in Channels of 
Constant Section. — Let aa', bV (fig. 103) be two cross sections normal 
to the direction of motion at a distance dl. Since the mass aa'bb' 
moves uniformly, the external forces acting on it are in equilibrium. 
Let U be the area of the cross sections, x the wetted perimeter, 



Fig. 102. 




t W 




Fig. 103. 



pa-{-qr-\-rs, of a section. Then the quantity m = £l/x is termed the 
hydraulic mean depth of the section. Let v be the mean velocity 
of the stream, which is taken as the common velocity of all the 
particles, i, the slope or fall of the stream in feet, per foot, being 
the ratio bejab. 

The external forces acting on aa'bb' parallel to the direction of 
motion are three: — (a) The pressures on aa' and bb', which are 
equal and opposite since the sections are equal and similar, and the 
mean pressures on each are the same, (b) The component of the 
weight \V of the mass in the direction of motion, acting at its centre 
of gravity g. The weight of the mass aa'bb' is GQdl, and the com- 
ponent of the weight in the direction of motion is GildlX the cosine of 
the angle between Wg and ab, that is, Gildl cos abc = GUdl bc/ab = 
GUidl. (c) There is the friction of the stream on the sides and 
bottom of the channel. This is proportional to the area x<U of 
rubbing surface and to a function of the velocity which may be 
written f(v) : /(f) being the friction per sq. ft. at a velocity v. Hence 
the friction is —xdlf(v). Equating the sum of the forces to zero, 
Gfii dl — xdlf(v)=o, 

f(v)/G = ai/x = mi. (1) 

But it has been already shown (§ 66) that/(») = fGf 2 / 2 g, 

.'. ff 2 /2g = mi. (2) 

This may be put in the form 

v = V(2g/f)V (mi) =cV ("»»'); (2a) 

where c is a coefficient depending on the roughness and form of the 
channel. 

The coefficient of friction f varies greatly with the degree of 
roughness of the channel sides, and somewhat also with the velocity. 
It must also be made to depend on the absolute dimensions of the 
section, to eliminate the error of neglecting the variations of velocity 
in the cross section. A common mean value assumed for f is 0-00757. 
The range of values will be discussed presently. 

It is often convenient to estimate the fall of the stream in feet per 
mile, instead of in feet per foot. If/ is the fall in feet per mile f 

/ = 52801. 
Putting this and the above value of f in (2a), we get the very simple 
and long-known approximate formula for the mean velocity of a 
stream — 

v = \y{2tnf). _ (3) 

The flow down the stream per second, or discharge of the stream, 
is Q = S2f = f2fV (mi). (4) 

§ 97. Coefficient of Friction for O-ben Channels. — Various ex- 
pressions have been proposed for cne coefficient of friction ior 
channels as .'„r pipes. Weisbach, giving attention chiefly to the 



In using this value of f when v is not known, it is best to proceed 
by approximation. 

§ 98. Darcy and Bazin's Expression for the Coefficient of Friction. — 
Darcy and Bazin's researches have shown that f varies very greatly 
for different degrees of roughness of the channel bed, and that it 
also varies with the dimensions of the channel. They give for f an 
empirical expression (similar to that for pipes) of the form 

f = a(l+/8/w); (6) 

where m is the hydraulic mean depth. For different kinds of 
channels they give the following values of the coefficient of friction : — 



Kind of Channel. 


a 


18 


I. Very smooth channels, sides of smooth 

cement or planed timber 

II. Smooth channels, sides of ashlar, brick- 
work, planks 

III. Rough channels, sides of rubble masonry or 

pitched w4th stone 

IV. Very rough canals in earth 

V. Torrential streams encumbered with detritus 


0-00294 

0-00373 

0-00471 
0-00549 
0-00785 


O-IO 

0-23 

0-82 
4-10 

5-74 



The last values (Class V.) are not Darcy and Bazin's, but are taken 
from experiments by Ganguillet and Kutter on Swiss streams. 

The following table very much facilitates the calculation of the 
mean velocity and discharge of channels, when Darcy and Bazin's 
value of the coefficient of friction is used. Taking the general 
formula for the mean velocity already given in equation (20) above, 

v = cy[ (mi), 
where c = V (2g/f), the following table gives values of c for channels 
of different degrees of roughness, and for such values of the hydraulic 
mean depths as are likely to occur in practical calculations : — 

Values ofc in v = cV (mi), deduced from Darcy and Bazin's Values. 



a 
u II 






c « 
§1 


%3 
■S3 


J3 r 2 


si 

2£ 


a 




8 e 

c tn 


"a3 . 

C-a 


SE.3 


3:5 


usq 


ug 


j=.S 


"S-3- 13 


3-5 


m . 


Cm 


J3.9 


■5 -3 -a 




si 

> rf 
O 






= -3 

rt 
> 


■sl'1 


a a, 


> C 
O 


■3 
m 
ni 
S3 


•S-o 
n 


3 — 

2 

> 


$ a z 

l.S-3 
Aug 


•25 


125 


95 


57 


26 


i8-5 


8-5 


147 


130 


112 


89 




•5 


135 


no 


72 


36 


25-6 


9-0 


147 


130 


112 


90 


7i 


•75 


139 


lib 


81 


42 


30-8 


9-5 


147 


130 


112 


90 




1-0 


141 


119 


87 


48 


34-9 


100 


147 


130 


112 


91 


72 


i-5 


143 


122 


94 


56 


41-2 


11 


147 


130 


113 


92 




2-0 


144 


124 


98 


62 


46-0 


12 


147 


130 


113 


93 


74 


2-5 


145 


126 


101 


67 




13 


147 


130 


"3 


94 




3-0 


H5 


126 


104 


70 


53 


H 


147 


130 


113 


95 




3-5 


146 


127 


105 


73 




15 


147 


130 


114 


96 


77 


4-0 


146 


128 


106 


76 


58 


16 


147 


130 


II4 


97 




4-5 


146 


128 


107 


78 




17 


147 


130 


114 


97 




5-0 


146 


128 


108 


80 


62 


18 


147 


130 


II4 


98 




,V5 


146 


129 


109 


82 




20 


147 


131 


II4 


98 


80 


6-0 


147 


129 


no 


«4 


65 


25 


I48 


131 


"5 


100 




6-5 


H7 


129 


no 


«5 




30 


148 


131 


"5 


102 


8.3 


7-0 


147 


129 


no 


8b 


67 


40 


I48 


I.3I 


116 


103 


8.5 


7-5 


H7 


129 


in 


87 




5° 


I48 


I.3I 


lib 


104 


86 


8-0 


147 


130 


in 


88 


69 


00 


I48 


131 


117 


108 


91 



§ 99. Ganguillet and Kutter's Modified Darcy Formula. — Starting 
from the general expression v = c^mi, Ganguillet and Kutter 
examined the variations of c for a wider variety of cases than those 
discussed by Darcy and Bazin. Darcy and Bazin's experiments 
were confined to channels of moderate section, and to a limited 
variation of slope. Ganguillet and Kutter brcugnt into the dis- 
cussion two very distinct and important additional series of results. 
The gaugings of the Mississippi by A. A. Humphreys and H. L. 
Abbot afford data of discharge for the case of a stream of exceotion- 
ally large section and or very low slope, on tne otner nana, their 
own measurements of the flow in the regulated channels of some 



7° 



HYDRAULICS 



[FLOW IN RIVERS 



Swiss torrents gave data for cases in which the inclination and 
roughness of the channels were exceptionally great. Darcy and 
Bazin's experiments alone were conclusive as to the dependence of 
the coefficient c on the dimensions of the channel and on its rough- 
ness of surface. Plotting values of c for channels of different in- 
clination appeared to indicate that it also depended on the slope of 
the stream. Taking the Mississippi data only, they found 

£ = 256 for an inclination of 0-0034 per thousand, 
= 154 .. .. °-° 2 .... 

so that for very low inclinations no constant value of c independent 
of the slope would furnish good values of the discharge. In small 
rivers, on the other hand, the values of c vary little with the slope. 
As regards the influence of roughness of the sides of the channel a 
different law holds. For very small channels differences of rough- 
ness have a great influence on the discharge, but for very large 
channels different degrees of roughness have but little influence, and 
for indefinitely large channels the influence of different degrees of 
roughness must be assumed to vanish. The coefficients given by 
Darcy and Bazin are different for each of the classes of channels of 
different roughness, even when the dimensions of the channel are 
infinite. But, as it is much more'probable that the influence of the 
nature of the sides diminishes indefinitely as the channel is larger, 
this must be regarded as a defect in their formula. 

Comparing their own measurements in torrential streams in 
Switzerland with those of Darcy and Bazin, Ganguillet and Kutter 
found that the four classes of coefficients proposed by Darcy and 
Bazin were insufficient to cover all cases. Some of the Swiss streams 
gave results which showed that the roughness of the' bed was 
markedly greater than in any of the channels tried by the French 
engineers. It was necessary therefore in adopting the plan of 
arranging the different channels in classes of approximately similar 
roughness to increase the number of classes. Especially an additional 
class was required for channels obstructed by detritus. 

To obtain a new expression for the coefficient in the formula 
z> = V (2g/f)V {mi) =cV {mi), 
Ganguillet and Kutter proceeded in a purely empirical way. They 
found that an expression of the form 

c = o/(i+(S/V»0 
could be made to fit the experiments somewhat better than Darcy's 
expression. Inverting this, we get 

l/c = l/a+/S/aV»», 
an equation to a straight line having i/Vwz for abscissa, i/c for 
ordinate, and inclined to the axis of abscissae at an angle the tangent 
of which is /3/o. 

Plotting the experimental values of l/c and i/V m, the points so 
found indicated a curved rather than a straight line, so that /3 must 
depend on o. After much comparison the following form was 
arrived at — 

c = (A+//»)/(i -f-A»/V m), 
where 11 is a coefficient depending only on the roughness o| the sides 
of the channel, and A and / are new coefficients, the value of which 
remains to be determined. From what has been already stated, the 
coefficient c depends on the inclination of the stream, decreasing as 
the slope i increases. 
Let A = a+p/i. 

Then c = (a+l/n+p/i)/li + {a-{-p/i)n/^m.}, 

the form of the expression for c ultimately adopted by Ganguillet 
and Kutter. 

For the constants a, /, p Ganguillet and Kutter obtain the values 
23, 1 and 0-00155 for metrical measures, or 41-6, i-8n and 0-00281 
for English feet. The coefficient of roughness n is found to vary 
from 0-008 to 0-050 for either metrical or English measures. 

The most practically useful values of the coefficient of roughness n 
are given in the following table : — 

Nature of Sides of Channel. Coefficient of 

Roughness ». 

Well-planed timber 0-009 

Cement plaster o-oio 

Plaster of cement with one-third sand .... o-oi I 

Unplaned planks 0-012 

Ashlar and brickwork 0-013 

Canvas on frames 0-015 

Rubble masonry 0-017 

Canals in very firm gravel 0-020 

Rivers and canals in perfect order, free from stones ) 

or weeds \ 

Rivers and canals in moderately good order, not / _ 

quite free from stones and weeds . . . . \ 
Rivers and canals in bad order, with weeds and , „ „ 

detritus _ \ °-°35 

Torrential streams encumbered with detritus . . 0-050 

Ganguillet and Kutter's formula is so cumbrous that it is difficult 
to use without the aid of tables. 

Lowis D'A. Jackson published complete and extensive tables for 
facilitating the use of the Ganguillet and Kutter formula {Canal 



and Culvert Tables, London, 1878). To lessen calculation he puts the 
formula in this form : — 

M =n(4.i-6-\-0-0028i (i) • 
z> = (Vm/»)l(M + i-8ii)/(M+Vm))V (»*')• 
The following table gives a selection of values of M, taken from 
Jackson's tables: — 



'•025 
3-030 



i — 


Values of M for n — 


O-OIO 


0-012 


0-015 


0-017 


0-020 


0-025 


OO3O 


•0000 1 


3-2260 


3-8712 


4-8390 


5-4842 


6-4520 


8-0650 


9-6780 


•00002 


I-82IO 


2-1852 


2-73I5 


3-0957 


3-6420 


4-5525 


5-4630 


•00004 


1-1185 


1-3422 


1-6777 


1-9014 


2-2370 


2-7962 


3-3555 


•00006 


0-8843 


1-0612 


1-3264 


1-5033 


1-7686 


2-2107 


2-6529 


•00008 


0-7672 


0-9206 


1-1508 


1-3042 


1-5344 


1-9180 


2-3016 


•OOOIO 


0-6970 


0-8364 


1 -0455 


1 • 1 849 


1-3940 


1-7425 


2-0910 


•00025 


0-5284 


0-6341 


0-7926 


0-8983 


1-0568 


1-3210 


1-5852 


•00050 


0-4722 


0-5666 


0-7083 


0-8027 


0-9444 


1-1805 


1-4166 


•00075 


0-4535 


0-5442 


0-6802 


0-7709 


0-9070 


I-I337 


1-3605 


•OOIOO 


0-4441 


0-5329 


o-666i 


0-7550 


0-8882 


I-II02 


1-3323 


•00200 


0-4300 


0-5160 


0-6450 


0-7310 


o-86oo 


1-0750 


1-2900 


•00300 


0-4254 


0-5105 


0-6381 


0-7232 


0-8508 


I-0635 


1-2762 



A difficulty in the use of this formula is the selection of the co- 
efficient of roughness. The difficulty is one which no theory will 
overcome, because no absolute measure of the roughness of stream 
beds is possible. For channels lined with timber or masonry the 
difficulty is not so great. The constants in that case are few and 
sufficiently defined. But in the case of ordinary canals and rivers the 
case is different, the coefficients having a much greater range. For 
artificial canals in rammed earth or gravel n varies from o 0163 to 
0-0301. For natural channels or rivers » varies from 0-020 to 0-035. 

In Jackson's opinion even Kutter's numerous classes of channels 
seem inadequately graduated, and he proposes for artificial canals 
the following classification : — 

I. Canals in very firm gravel, in perfect order w = o-02 

II. Canals in earth, above the average in order ^ = 0-0225 
III. Canals in earth, in fair order .... n =0-025 

■ IV. Canals in earth, below the average in order n = 0-0275 

V. Canalsin earth, inratherbad order, partially ) 

overgrown with weeds and obstructed by > n = 0-03 

detritus . . ' 

Ganguillet and Kutter's formula has been considerably used 
partly from its adoption in calculating tables for irrigation work in 
India. But it is an empirical formula of an unsatisfactory form. 
Some engineers apparently have assumed that because it is com- 
plicated it must be more accurate than simpler formulae. Com- 
parison with the results of gaugings shows that this is not the case. 
The term involving the slope was introduced to secure agreement 
with some early experiments on the Mississippi, and there is strong 
reason for doubting the accuracy of these results. 

§ 100. Bazin's New Formula. — Bazin subsequently re-examined 
all the trustworthy gaugings of flow in channels and proposed a 
modification of the original Darcy formula which appears to be 
more satisfactory than any hitherto suggested {iLtude d'une nouvelle 
formule, Paris, 1898). He points out that Darcy's original formula, 
which is of the form mi/v 2 = a-}-p/m, does not agree with experiments 
on channels as well as with experiments on pipes. It is an objection 
to it that if m increases indefinitely the limit towards which mi/v 2 
tends is different for different values of the roughness. It would 
seem that if the dimensions of a canal are indefinitely increased the 
variation of resistance due to differing roughness should vanish. 
This objection is met if it is assumed that V {mijv 1 ) =a-f-/3/Vm, 
so that if a is a constant mi/v* tends to the limit a when m increases. 
A very careful discussion of the results of gaugings shows that they 
can be expressed more satisfactorily by this new formula than by 
Ganguillet and Kutter's. Putting the equation in the form $> l l2g = 
mi, f = 0-002594(1 +7/Vm), where y has the following values: — 
I. Very smooth sides, cement, planed plank, 7= 0-109 

II. Smooth sides, planks, brickwork .... 0-290 

III. Rubble masonry sides 0-833 

IV. Sides of very smooth earth, or pitching . . 1-539 
V. Canals in earth in ordinary condition . . . 2-353 

VI. Canals in earth exceptionally rough . . . 3-168 

§ 101. The Vertical Velocity Curve. — If at each point along -a 
vertical representing the depth of a stream, the velocity at that 
point is plotted horizontally, the curve obtained is the vertical 
velocity curve and it has been shown by many observations that 
it approximates to a parabola with horizontal axis. The vertex of 
the parabola is at the level of the greatest velocity. Thus in fig. 104 
OA is the vertical at which velocities are observed ; v is the sur- 
face; v z the maximum and Vd the bottom velocity. B C D is the 
vertical velocity curve which corresponds with a parabola having its 
vertex at C. The mean velocity at the vertical is 

Vm = \\2V z +V d -\- {dz/d) (»„ —Vd)]. 

The Horizontal Velocity Curve. — Similarly if at each point along a 
horizontal representing the width of the stream the velocities are 



AND CANALS] 



HYDRAULICS 



7 



plotted, a curve is obtained called the horizontal velocity curve. 
In streams of symmetrical section this is a curve symmetrical about 
the centre line of the stream. The velocity varies little near the 
centre of the stream, but very rapidly near the banks. In un- 

symmetrical sections the greatest 
velocity is at the point where the 
stream is deepest, and the general 
form of the horizontal velocity curve 
is roughly similar to the section of 
the stream. 

§ 102. Curves or Contours of Equal 
Velocity. — If velocities are observed 
at a number of points at different 
widths and depths in a stream, it is 
possible to draw curves on the cross 
section through points at which the 
velocity is the same. These repre- 
sent contours of a solid, the volume 
of which is the discharge of the 
stream per second. Fig. 105 shows 
the vertical and horizontal velocity curves and the contours of 
equal velocity in a rectangular channel, from one of Bazin's 
gaugings. 

§ 103. Experimental Observations on the Vertical Velocity Curve. — 
A preliminary difficulty arises in observing the velocity at a given 
point in a stream because the velocity rapidly varies, the motion 
not being strictly steady. If an average of several velocities at the 
same point is taken, or the average velocity for a sensible period of 
time, this average is found to be constant. It may be inferred that 




Fig. 104. 



.1 .-' 



""1' 



Vertical Velocity [ 
Curves 









• i Horizontal Velocity Cuijves ; I 

* 1 < i i , 1 1 ' 




►1 

I Vertical Velocity 
I Curves 



e f g h i j k 
Contours of Ecjual Velocity 

Fig. 105. 

though the velocity at a point fluctuates about a mean value, the 
fluctuations being due to eddying motions superposed on the general 
motion of the stream, yet these fluctuations produce effects which 
disappear in the mean of a series of observations and, in calculating 
the volume of flow, may be disregarded. 

In the next place it is found that in most of the best observations 
on the velocity in streams, the greatest velocity at any vertical is 
found not at the surface but at some distance below it. In various 
river gaugings the depth d z at the centre of the stream has been found 
to vary from o to o-^d. 

§ 104. Influence of tlie Wind. — In the experiments on the Missis- 
sippi the vertical velocity curve in calm weather was found to agree 
fairly with a parabola, the greatest velocity being at i^ths of the 
depth of the stream from the surface. With a wind blowing down 
stream the surface velocity is increased, and the axis of the parabola 
approaches the surface. On the contrary, with a wind blowing up 
stream the surface velocity is diminished, and the axis of the para- 
bola is lowered, sometimes to half the depth of the stream. The 
American observers drew from their observations the conclusion 
that there was an energetic retarding action at the surface of a 
stream like that due to the bottom and sides. If there were such 
a retarding action the position of the filament of maximum velocity 
below the surface would be explained. 

It is not difficult to understand that a wind acting on surface 
ripples or waves should accelerate or retard the surface motion of 
the stream, and the Mississippi results may be accepted so far as 
showing that the surface velocity of a stream is variable when the 
mean velocity of the stream is constant. Hence observations of 
surface velocity by floats or otherwise should only be made in very 
calm weather. But it is very difficult to suppose that, in still air, 
there is a resistance at the free surface of the stream at all analogous 
to that at the sides and bottom. Further, in very careful experi- 
ments, P. P. Boileau found the maximum velocity, though raised a 
little above its position for calm weather, still at a considerable 
distance below the surface, even when the wind was blowing down 
stream with a velocity greater than that of the stream, and when 
the action of the air must have been an accelerating and not a re- 
tarding action. A much more probable explanation of the diminution 



of the velocity at and near the free surface is that portions of water, 
with a diminished velocity from retardation by the sides or bottom, 
are thrown off in eddying masses and mingle with the rest of the 
stream. These eddying masses modify the velocity in all parts of 
the stream, but have their greatest influence at the free surface. 
Reaching the free surface they spread out and remain there, mingling 
with the water at that level and diminishing the velocity which would 
otherwise be found there. 

Influence of the Wind on the Depth at which the Maximum Velocity 
is found. — In the gaugings of the Mississippi the vertical velocity 
curve was found to agree well with a parabola having a horizontal 
axis at some distance below the water surface, the ordinate of the 
parabola at the axis being the maximum velocity of the section. 
During the gaugings the force of the wind was registered on a scale 
ranging from o for a calm to 10 for a hurricane. Arranging the 
velocity curves in three sets — (1) with the wind blowing up stream, 
(2) with the wind blowing down stream, (3) calm or wind blowing 
across stream — it was found that an up-stream wind lowered, and 
a down-stream wind raised, the axis of the parabolic velocity curve. 
In calm weather the axis was at j^ths of the total depth from the 
surface for all conditions of the stream. 

Let h' be the depth of the axis of the parabola, m the hydraulic 
mean depth, / the number expressing the force of the wind, which 
may range from + 10 to — 10, positive if the wind is up stream, 
negative if it is down stream. Then Humphreys and Abbot find 
their results agree with the expression 

h'/m = 0-3 1 7 ± 0-06/. 
Fig. 106 shows the parabolic velocity curves according to the 
American observers for calm weather, and for an up- or down-stream 
wind of a force represented by 4. 




Fig. 106. 

It is impossible at present to give a theoretical rule for the vertical 
velocity curve, but in very many gaugings it has been found that a 
parabola with horizontal axis fits the observed results fairly well. 
The mean velocity on any vertical in a stream varies from 0-85 to 
0-0,2 of the surface velocity at that vertical, and on the average if v 
is the surface and Vm the mean velocity at a vertical v m = %v , a result 
useful in float gauging. On any vertical there is a point at which 
the velocity is equal to the mean velocity, and if this point were 
known it would be useful in gauging. Humphreys and Abbot in 
the Mississippi found the mean velocity at o-66 of the depth ; G. H. L. 
Hagen and H. Heinemann at 0-56 to 0-58 of the depth. The mean 
of observations by various observers gave the mean velocity at from 
0-587 to 0-62 of the depth, the average of all being almost exactly 
0-6 of the depth. The mid-depth velocity is therefore nearly equal 
to, but a little greater than, the mean velocity on a vertical. If 
Vmd is the mid-depth velocity, then on the average v m = o-g8v md . 

§ 105. Mean Velocity on a Vertical from Two Velocity Observations. 
— A. J. C. Cunningham, in gaugings on the Ganges canal, found the 
following useful results. Let v be the surface, v m the mean, and 
v x d the velocity at the depth xd ; then 

am = iOo+3»2/3<;) 

= h(v.m d +v. 7 M d ). 
§ 106. Ratio of Mean to Greatest Surface Velocity, for the whole 
Cross Section in Trapezoidal Channels. — It is often very important 
to be able to deduce the mean velocity, and thence the discharge, 
from observation of the greatest surface velocity. The simplest 
method of gauging small streams and channels is to observe the 
greatest surface velocity by floats, and thence to deduce the mean 
velocity. In general in streams of fairly regular section the mean 
velocity for the whole section varies from 0-7 'to 0-85 of the greatest 
surface velocity. For channels not widely differing from those 
experimented on by Bazin, the expression obtained by him for the 
ratio of surface to mean velocity may be relied on as at least a good 
approximation to the truth. Let v be the greatest surface velocity, 
v m the mean velocity of the stream. Then, according to Bazin, 

v m = v — 25-4 V {mi). 
But v m = c^J (mi), 

where c is a coefficient, the values of which have been already given 
in the table in § 98. Hence 

»m = tW(c+25-4). 



72 



HYDRAULICS 



[FLOW IN RIVERS 



Values of Coefficient cl{c-\-2§-$) in the Formula v m =cv /(c+2^-^) 



Hydraulic 
Mean Depth 


Very 


Smooth 


Rough 


Very Rough 


Channels 


Smooth 


Channels. 


Channels. 


Channels. 


encumbered 


Channels. 


Ashlar or 


Rubble 


Canals in 


with 




Cement. 


Brickwork. 


Masonry. 


Earth. 


Detritus. 


0-25 


•83 


•79 


•69 


■51 


•42 


o-5 


•84 


•81 


•74 


•58 


•50 


o-75 


■84 


•82 


•76 


•63 


•55 


1-0 


•85 




•77 


•65 


■58 


2-0 




•83 


•79 


•71 


■64 


3-0 






■80 


•73 


•67 


4-o 






•81 


•75 


•70 


5-o 








•76 


•71 


6o 




•8 4 




•77 


•72 


7-o 








•78 


•73 


8-o 












9-o 






•82 




•74 


10-0 












15-0 








•79 


•75 


20-0 








•80 


•76 


300 






•82 




•77 


40-0 












500 












00 










•79 



general mass of water must flow outwards to take its place. Fig. 107 
shows the directions of flow as observed in a small artificial stream, 
by means of light seeds and specks of aniline dye. The lines CC 
show the directions of flow immediately in contact with the sides 
and bottom. The dotted line AB shows the direction of motion of 
floating particles on the surface of the stream. 

§ 108. Discharge of a River when flowing at different Depths. — 
When frequent observations must be made on the flow of a river 
or canal, the depth of which varies at different times, it is very 
convenient to have to observe the depth only. A formula can be 
established giving the flow in terms of the depth. Let Q be the 
discharge in cubic feet per second ; H the depth of the river in some 
straight and uniform part. Then Q = aH + &H 2 , where the constants 
a and b must be found by preliminary gaugings in different con- 
ditions of the river. M. C. Moquerey found for part of the upper 
Saone, Q = 64-71! +8-2H 2 in metric measures, or Q = 696H+26-8H 2 
in English measures. 

§ 109. Forms of Section of Channels. — The simplest form of section 
for channels is the semicircular or nearly semicircular channel (fig. 
log), a form now often adopted from the facility with which it can be 



§ 107. River Bends. — In rivers flowing in alluvial plains, the wind- 
ings which already exist tend to increase in curvature by the scouring 
away of material from the outer bank and the deposition of detritus 
along the inner bank. The sinuosities sometimes increase till a 
loop is formed with only a narrow strip of land between the two 
encroaching branches of the river. Finally a " cut off " may occur, 
a waterway being opened through the strip of land and the loop 

left separated from the 
iCWMillim^^ stream, forming a horse- 

"-*-""""'"■ shoe shaped lagoon or 

marsh. Professor James 
Thomson pointed out 
(Proc. Roy. Soc, 1877, 
p. 356; Proc. Inst, of 
Mech. Eng., 1879, p. 456) 
that the usual supposi- 
tion is that the water 
jy tending to go forwards 
in a straight line rushes 
against the outer bank 
and scours it, at the 
same time creating de- 
posits at the inner bank. 
That view is very far 
from a complete account 
of the matter, and Pro- 
fessor Thomson gave a 
p much more ingenious 

' ' account of the action at 

the bend, which he completely confirmed by experiment. 

When water moves round a circular curve under the action of 
gravity only, it takes a motion like that in a free vortex. Its velocity 
is greater parallel to the axis of the stream at the inner than at the 
outer side of the bend. Hence the scouring at the outer side and 
the deposit at the inner side of the bend are not due to mere difference 
of velocity of flow in the general direction of the stream; but, in 
virtue of the centrifugal force, the water passing round the bend 
presses outwards, and the free surface in a radial cross section has 
a slope from the inner side upwards to the outer side (fig. 108). 
For the greater part of the water flowing in curved paths, this 
difference of pressure produces no tendency to transverse motion. 

But the water im- 
Inner Bank 




Outer Bank 



mediately in contact 
with the rough bot- 
tom and sides of the 
channel is retarded, 
and its centrifugal 
force is insufficient to 
balance the pressure 
due to the greater 
depth at the outside 
of the bend. It there- 
fore flows inwards towards the inner side of the bend, carrying 
with it detritus which is deposited at the inner bank. Con- 
jointly with this flow inwards along the bottom and sides, the 




Section at M N. 
Fig. 108. 




Fig. 109. 

executed in concrete. It has the advantage that the rubbing surface 
is less in proportion to the area than in any other form. 

Wooden channels or flumes, of which there are examples on a 
large scale in America, are rectangular in section, and the same form 
is adopted for wrought and cast-iron aqueducts. Channels built 
with brickwork or masonry may be also rectangular, but they 
are often trapezoidal, and are always so if the sides are pitched 
with masonry laid dry. In a trapezoidal channel, let b (fig. no) 



l^. . 


% = 2£ 








vFwj-rzEr- 




"^ 


1= 


: :3£E^f^y 









— 










J i 








^■5^vjYjQS2 


nanrrmfei 






YrTflPj:£-'pr~C 



Concrete 
Fig. no. 

be the bottom breadth, 6 the top breadth, d the depth, and let 
the slope of the sides be n horizontal to 1 vertical. Then the area 
of section is fl = {b+nd)d — (b — nd)d, and the wetted perimeter 
X = b+2d V(» ! + l). 

When a channel is simply excavated in earth it is always 
originally trapezoidal, though it becomes more or less rounded in 
course of time. The slope of the sides then depends on the 
stability of the earth, a slope of 2 to 1 being the one most 
commonly adopted. 

Figs, in, 112 show the form of canals excavated in earth, the 
former being the section of a navigation canal and the latter the 
section of an irrigation canal. 

§110. Channels of Circular Section. — The following short table 
facilitates calculations of the discharge with different depths of water 
in the channel. Let r be the radius of the channel section; then 
for a depth of water = «r, the hydraulic mean radius is /xr and the 
area of section of the waterway vr 2 , where k, m. and v have* the 
following values : — 



Depth of water in ) _ 
terms of radius . . ) ~ 


.01 


•OS 


.10 


■IS 


.20 


■25 


■30 


■3S 


.40 


•45 


•SO 


•S5 


.60 


• 65 


.70 


•75 


.80 


•85 


.90 


■95 


1.0 


Hydraulic mean depth ) _ 
in termsof radius . S 


.00668 


.0321 


■0523 


.0963 


.1278 


■ 1574 


■ I8S2 


.2142 


.242 


.269 


■ 293 


.320 


■343 


■ 365 


.387 


.408 


.429 


■ 449 


.466 


.484 


■ Soo 


Waterway in terms of ( v _ 
square of radius . . ) 


.00189 


.0211 


•0598 


.1067 


.i6si 


.228 


.294 


•370 


■450 


■S3 2 


.614 


.709 


■795 


.885 


■979 


I-C75 


I-I75 


1.276 


I-37I 


1.470 


1. 571 



AND CANALS] 



HYDRAULICS 



73 



§ in. Egg-Shaped Channels or Sewers. — In sewers for discharging | could be found satisfying the foregoing conditions. To render 



storm water and house drainage the volume of flow is extremely 
variable ; and there is a great liability for deposits to be left when 
the flow is small, which are not removed during the short periods 
when the flow is large. The sewer in consequence becomes choked. 



a given discharge Oco y/ x, 
amount of excavation will 
the least wetted perimeter. 



In Bank 



In Cutti 




Fig. i ii. — Scale 20 ft. = 1 in. 





Fig. 112. — Scale 80 ft. = 1 in. 

To obtain uniform scouring action, the velocity of flow should be 
constant or nearly so ; a complete uniformity of velocity cannot be 
obtained with any form of section suitable for sewers, but an ap- 
proximation to uniform velocity {s obtained by making the sewers 
of oval section. Various forms of oval have been suggested, the 

simplest being one in 
which the radius of the 
crown is double the radius 
of the invert, and the 
greatest width is two- 
thirds the height. The 
section of such a sewer I 
is shown in fig. 113, the 
numbers marked on the 
figure being proportional 
numbers. 

§ 112. Problems on 
Channels in which the 
Flow is Steady and at 
Uniform Velocity. — The 
general equations given 
in §§ 96, 98 are 

f = a(i+/S/m); (1) 
fi;2/2g =mi; (2) 

Fig- "3- Q = Qp. (3) 

Problem I. — Given the transverse section of stream and dis- 
charge, to find the slope. From the dimensions of the section 
find it and m; from (1) find f, from (3) find v, and lastly from (2) 
find i. 

Problem II. — Given the transverse section and slope, to find the 
discharge. Find v from (2), then Q from (3). 

Problem III. — Given the discharge and slope, and either the 
breadth, depth, or general form of the section of the channel, to 
determine its remaining dimensions. This must generally be solved 
by approximations. A breadth or depth or both are chosen, and 
the discharge calculated. If this is greater than the given discharge, 
the dimensions are reduced and the discharge recalculated. 

Since m lies generally between the limits m = d and m = \d, where j 
d is the depth of the stream, and since, moreover, the velocity 
varies as V (m) so that an error in the value of m leads only to a much 
less error in the value of the velocity calculated from it, we may 
proceed thus. Assume a value for m, and calculate v from it. 
Let i'i be this first approximation to v. Then Q/i'i is a first approxi- 
mation to SI, say fii. With this value of design the section of the 
channel ; calculate a second value for m ; calculate from it a second 

_^___ value of v, and from that a 

7 i\ " ~ ' i 7 second value for Q. Repeat 

the process till the succes- 
sive values of m approxi- 
mately coincide. 

§ 113. Problem IV. Most 

Economical Form of Channel 

p for given Side Slopes. — Sup- 

4- pose the channel is to be 

trapezoidal in section (fig. 114), and that the sides are to have a 

given slope. Let the longitudinal slope of the stream be given, 

and also the mean velocity. An infinite number of channels 



the problem determinate, let it be remembered that, since for 

other things being the same, the 

be least for that channel which has 

Let d be the depth and b the bottom 

width of the channel, and let the 

sides slope n horizontal to I vertical 

(fig. 114), then 

tt = (b+nd)d; 
X-=i+2dV(re 2 + i). 
Both fi and x are to be minima. 
Differentiating, and equating to 
zero. 

(db/dd+n)d+b+nd = o, 
<26/<M+2V(» 2 + i)=o; 

eliminating db/dd, 

\n — 2V {ri l -\-i))d-\-b-\-nd=o; 
b = 2 {V (» 2 + i) — n)d. 
But 

a/ x = (b+nd)d/{b+2d^ (n 2 + l)]. 
Inserting the value of b, 
fi/x = |2rfV (n 2 + iy-nd}l 

UW(n* + i)-2nd] = hd. 

That is, with given side slopes, 

the section is least for a given 

discharge when the hydraulic mean 

depth is half the actual depth. 

A simple construction gives the 
form of the channel which fulfils 
shown that when m = id the sides 



this condition, for 
of the channel 
water line. 
Since 
therefore 



it can be 
are tangential 



to a semicircle drawn on the 



(I) 



n=hxd. 

Let ABCD be the channel (fig. 115) ; from E the centre of AD drop 

perpendiculars EF, EG, EH on the sides. 

Let 

AB=CD=o; BC = Z>; EF = EH=c; and EG=d. 
fi = area AEB+BEC+CED, 

= ac-\-\od. 
X = 2a+b. 

Putting these values in (1), 

ac-\-\bd={a J r\b)d; and hence c = d. 



E 




7D 



IB. 



Fig. 115. 
That is, EF, EG, EH are all equal, hence a semicircle struck 



io the depth of the stream will pass 



a 




--&.... 



from E with radius equal 
through F and H and be 
tangential to the sides of 
the channel. 

To draw the channel, 
describe a semicircle on 

a' horizontal line with , 

radius = depth of channel. k- -b- 

The bottom will be a Fig. 116. 

horizontal tangent of that 
semicircle, and the sides 
slopes. 

The above result may be obtained thus (fig. 116) :- 




tangents drawn at the required side 



x — b-{-2djs\n p. 

U = d(b+d cot p); 
il/d = b+d cot P; 
i2ld? = b/d+cotp. 



From (1) and (2), 

X = fi/<Z- 
This will be a minimum for 



■d cot |8+2rf/sin p. 



or 
or 



From (3) and (4), 



dx/dd = Q/d 2 +cot |8-2/sin/3 = o, 
il/d? = 2 cosec. P — cot p. 
d = V(fl sin 0/(2 -cos 0)). 



(1) 

(2) 
(3) 



(4) 



6/i = 2(l-cos/3)/sin p-2 tan \p. 



74 



HYDRAULICS 



[FLOW IN RIVERS 



Proportions of Channels of Maximum Discharge for given Area and 
Side Slopes. Depth of channel = d\ Hydraulic mean depth = id; 
Area of section = S2. 





Inclination 


Ratio of 
Side 


Area of 


Bottom 


Top width ~ 
twice length 




Horizon. 


Slopes. 


Section a. 


Width. 


of each Side 
Slope. 


Semicircle . 






1-571* 


O 


2d 


Semi-hexagon , 


60 ° 0' 


3 -5 


1-732* 


i-i55<* 


2-310(2 


Semi-square 


90 ° 0' 


: 1 


2* 


2d 


2(2 




75° 58' 


1 :4 


I-8I2* 


1 562*2 


2-062(2 




63° 26' 


1 : 2 


1-736* 


1-236(2 


2-236(2 




53° 8' 


3 :4 


1-750* 


d 


2-50O(2 




45° 0' 


1 : 1 


1-828* 


0-828<2 


2-828(2 




38° 40' 


li : 1 


1 -952* 


0-702*2 


3-202(2 




33° 42' 


ii : 1 


2- 106* 


o-6o6<2 


3-6o6<2 




29° 44' 


if :i 


2-282* 


o-532</ 


4-032(2 




26° 34' 


2 : 1 


2-472* 


0-472(2 


4-472(2 




23° 58 


2\: 1 


2-674* 


0-424(2 


4-924*2 




21° 48' 


2j :i 


2-885* 


0-385(2 


5-385d 




I 9 ° 58' 


2f : 1 


3-104* 


o-354<* 


5-854^ 




18 26' 


3 : 1 


3-325* | o-325<2 


6-325*2 



velocity and slope _are greatest. If in a stream of tolerably uniform 
slope an obstruction such as a weir is built, that will cause an altera- 
tion of flow similar to that of an alteration of the slope of the bed 
for a greater or less distance above the weir, and the originally uni- 
form cross section of the stream will become a varied one. In such 
cases it is often of much practical importance to determine the 
longitudinal section of the stream. 

The cases now considered will be those in which the changes of 
velocity and cross section are gradual and not abrupt, and in which 
the only internal work which needs to be taken into account is that 
due to the friction of the stream bed, as in cases of uniform motion. 
Further, the motion will be supposed to be steady, the mean velocity 
ateach given cross section remaining constant, though it varies from 
section to section along the course of the stream. 

Let fig. 118 represent a longitudinal section of the stream, A0A1 
being the water surface, ,BoBi the stream bed. Let A0B0, A1B1 be 



Half the top width is the length of each side slope. The wetted 
perimeter is the sum of the top and bottom widths 

§ 1 1 4. Form of Cross Section of Channel in which the Mean Velocity 
is Constant with Varying Discharge. — In designing waste channels 
from canals, and in some other cases, it is desirable that the mean 
velocity should be restricted within narrow limits with very different 
volumes of discharge. In channels of trapezoidal form the velocity 
increases and diminishes with the discharge. Hence when the 
discharge is large there is danger of erosion, and when it is small of 
silting or obstruction by weeds. A theoretical form of section for 
which the mean velocity would be constant can be found, and, 
although this is not very suitable for practical purposes, it can be 
more or less approximated to in actual channels. 

Let fig. 117 represent the cross section of the channel. From the 
symmetry of the section, only half the channel need be considered. 






Scale id Inch = 1 Foot- 
Fig. 117. 

Let obac be any section suitable for the minimum flow, and let it 
be required to find the curve beg for the upper part of the channel 
so that the mean velocity shall be constant. Take o as origin of 
coordinates, and let de, fg be two levels of the water above ob. 
Let ob = b(2 ; de = y, fg = y+dy, od = x, of=x+dx; eg = ds. 
The condition to be satisfied is that 
ii = cV {mi) 
should be constant, whether the water-level is at ob, de, or fg. Con- 
sequently 

m = constant = k 
for all three sections, and can be found from the section 060c. Hence 
also 

Increment of section ydx , 
Increment of perimeter - ds ~ 
y*dx> = k 2 ds 1 =:kHdx'-+dy*) and dx = kdyH {f-h?). 
Integrating, 

x-k \oge\y-\- V(y" — fe 1 ))+constant ; 
and, since y = b, ! 2 when x = o, 

.r = felog,[iy+V(y a -fc 2 )}/U&+va<y-fc 2 )}]. 
Assuming values for y, the values of x can be found and the curve 
drawn. 

The figure has been drawn for a channel the minimum section of 
which is a half hexagon of 4 ft. depth. Hence k = 2; 6 = 9-2; the 
rapid flattening of the side slopes is remarkable. 

Steady Motion of Water in Open Channels of Varying 
Cross Section and Slope 

§ 1 15. In every stream the discharge of which is constant, or may 
be regarded as constant for the time considered, the velocity at 
different places depends on the slope of the bed. Except at certain 
exceptional points the velocity will be greater as the slope of the 
bed is greater, and, as the velocity and cross section of the stream 
vary inversely, the section of the stream will be least where the 



Fig. 118. 

cross sections normal to the direction of flow. Suppose the mass 
of water A0B0A1B1 comes in a short time 8 to C0D0C1D1, and let the 
work done on the mass be equated to its change of kinetic energy 
during that period. Let / be the length A0A1 of the portion of the 
stream considered, and z the fall, of surface level in that distance. 
Let Q be the discharge of the stream per second. 

Change of Kinetic Energy. — At the end of the time 6 there are as 
many particles possessing the same velocities in the space C0D0A1B1 
as at the beginning. The 
change of kinetic energy is 
therefore the difference of 
the kinetic energies of 
A0B0C0D0 and A1B1GD1. 

Let fig. 119 represent the 
cross section A 6o, and let 
10 bea small element of its 
area at a point where the p 

velocity is v. Let S2o be the ' "' 

whole area of the cross section and «o the mean velocity for the 
whole cross section. From the definition of mean velocity we have 

«o=2u»/Qd. 
Let u = «o+w, where w is the difference between the velocity at the 
small element u and the mean velocity. For the whole cross section, 
2wtt> = o. 

The mass of fluid passing through the element of section w, in 8 
seconds, is (G/g)wv8, and its kinetic energy is (G/2g)uv 3 8. For the 
whole section, the kinetic energy of the mass A0B0C0D0 passing in 8 
seconds is 

(G0/2g)2«f s - (Gt9/2g)2a)(«o 3 +3«o 2 Jf+3«oie' 2 +w 3 ), 
= (Gt9/2£){»o 3 fl+2aja> 2 (3« +Kj)}. 
The factor 3U0+W is equal to 2Uo+v, a quantity necessarily 
positive. Consequently 2*oi l3 > fioWo 3 , and consequently the kinetic 
energy of A0B0C0D0 is greater than 

(G0/2g)ftotto 3 or (G8/2g)Qu \ 
which would be its value if all the particles passing the section had 
the same velocity #0. Let the kinetic energy be taken at 

o( G8/2g) SW = a(G0/2g) Q«o 2 , 
where a is a corrective factor, the value of which was estimated by 
J. B. C. J. Belanger at l-i. 1 Its precise value is not of great im- 
portance. 

In a similar way we should obtain for the kinetic energy of 
A 1 BiCiDj the expression 

a(G0/2g)»Ki 3 = a(Gf?/2g)Q«i 2 , 
where ft, «i are the section and mean velocity at AiBj, and where a 
may be taken to have the same value as before without any im- 
portant error. 

Hence the change of kinetic energy in the whole mass A0B0A1B1 
in 8 seconds is 

t(G6/2g)Q( Ml 2 -«o 2 ). (1) 

Motive Work of the Weight and Pressures. — Consider a small 
filament aodi which comes in 8 seconds to foci. The work done by 
gravity during that movement is the same as if the portion aoCo were 
carried to aiCi. Let dQ8 be the volume of aoco or a\c\, and yo, y\ the 
depths of do, <zi from the surface of the stream. Then the volume 

1 Boussinesq has shown that this mode of determining the corrective 
factor a is not satisfactory. 



AND CANALS] 



HYDRAULICS 



75 



and 



dQ9 or GdQd pounds falls through a vertical height z+yi—yo, 
the work done by gravity is 

GdQ8(z+ yi -y ). 
Putting pa for atmospheric pressure, the whole pressure per unit of 
area at ao is Gyo+p a , and that at Oi is — (Gyi+pa). The work of 
these pressures is 

G(y<,+p./G-y 1 -palG)dQ8 = G{y a -y 1 )dQB. 
Adding this to the work of gravity, the whole work is GzdQB; or, 
for the whole cross section, 

GsQ0. _ (2) 

Work expended in Overcoming the Friction of the Stream Bed. — 
Let A'B', A"B" be two cross sections at distances s and s-j-ds from 
AoBo. Between these sections the velocity may be treated as uni- 
form, because by hypothesis the changes of velocity from section 
to section are gradual. Hence, to this short length of stream the 
equation for uniform motion is applicable. But in that case the 
work in overcoming the friction of the stream bed between A'B' and 
A"B"is 

GQ0r(« 2 /2|i)(x/a)</s, 
where u, x, S2 are the mean velocity, wetted perimeter, and section 
at A'B'. Hence the whole work lost in friction from AoBo to A1B1 
will be 

(3) 



;GQfl/ o V(« 2 /2g)(x/n)^. 



Equating the work given in (2) and (3) to the change of kinetic 
energy given in (1), 

a(GQ0/ 2 g) («, 2 -W) =GQ30-GQe/- o 'r(«72g)(x/a)<fr; 
.-. z = a( Ul '-tu?)l2g+fj:(uV2g) (x/tyds. 

§ 116. Fundamental Differential Equation of Steady VariedMotion. — 
Suppose the equation just found to be applied to an indefinitely 
short length ds of the stream, limited by the end sections ab, 0161, 
taken for simplicity normal to the stream bed (fig. 120). For that 
short length of stream the fall of surface level, or difference of level of 




BoBi the bed in a longitudinal section of the stream, and ab any 
section at a distance 5 from Bo, the depth ab being h. Suppose 
B0B1, B0A0 taken as rectangular coordinate axes, then dh/ds is the 
trigonometric tangent of the angle which the surface of the stream 
at a makes with the axis BoBi_ This tangent dh/ds will be positive, 
if the stream is increasing in depth in the direction B0B1; negative, 



Fig. 120. 

o and ai, may be written dz. Also, if we write u for uo, and u+du for 
«i, the term (wo 2 — tti 2 )/2g becomes udu/g. Hence the equation 
applicable to an indefinitely short length of the stream is 

dz = udulg + (xlil)t( u y2g)ds. _ (1) 

From this equation some general conclusions may be arrived at as 
to the form of the longitudinal section of the stream, but, as the 
investigation is somewhat complicated, it is convenient to simplify 
it by restricting the conditions of the problem. 

Modification of the Formula for the Restricted Case of a Stream 
flowing in a Prismatic Stream Bed of Constant Slope. — Let i be 
the constant slope of the bed. Draw ad parallel to the bed, and ac 
horizontal. Then dz is sensibly equal to a'c. The depths of the 
stream, h and h-\-dh, are sensibly equal to ab and a'b' , and therefore 
dh—a'd. Also cd is the fall of the bed in the distance ds, and is 
equal to ids. Hence 

dz = a'c=cd—a'd = ids—dh. (2) 

Since the motion is steady — 

Q =Uu = constant. 
Differentiating, 

ildu + udil = o ; 
:.du= — udtt/Q. 
Let x be the width of the stream, then dXl=xdh very nearly. In- 
serting this value, 

du — —{uxi\i)dh. (3) 

Putting the values of du and dz fouftd in (2) and (3) in equation (1), 
ids-dh = - {u i xl0.l)dh + (xl^)i{u 1 l2g)ds. 
dhlds = {i-( x lil)!;(u>l2g)\l\i-Wg)(xln).\ (4) 

Further Restriction to the Case of a Stream of Rectangular Section 
and of Indefinite Width. — The equation might be discussed in the 
form just given, but it becomes a little simpler if restricted in the 
way just stated. For, if the stream is rectangular, xh = Q, and if x 
is large compared with h, tt/x = xh/x = h nearly. Then equation (4) 
becomes 

dh/ds = ((i -r« 2 /2g*)/(i -u*/gh). (5) 

§ 117. General Indications as to the Form of Water Surface fur- 
nished by Equation (5). — Let A0A1 (fig. 121) be the water surface, 




Fig. 121. 

if the stream is diminishing in depth from Bo towards Bi. If dh/ds = 0, 
the surface of the stream is parallel to the bed, as in cases of uniform 
motion. But from equation (4) 

dh/ds = o, if ;-(x/S2)f(w 2 /2g)=o; 
.". f(w 2 /2g) = (O/xH = mi, 
which is the well-known general equation for uniform motion, based 
on the same assumptions as the equation for varied steady motion 
now being considered. The case of uniform motion is therefore a 
limiting case between two different kinds of varied motion. 
Consider the possible changes of value of the fraction 

{l-W/2gih)l{l-li>lgh). 

As h tends towards the limit o, and consequently « is large, the 
numerator tends to the limit — 00. On the other hand if h = <x>, in 
which case u is small, the numerator becomes equal to I. For a 
value H of h given by the equation 

l-f«72gi'H=o, 
H=f« 2 /2gi, 
we fall upon the case of uniform motion. The results just stated 
may be tabulated thus : — 

For h=o, H, >H, <x , 
the numerator has the value — 00, o, > o, 1. 

Next consider the denominator, if h becomes very small, in which 
case u must be very large, the denominator tends to the limit — 00 . 
As h becomes very large and u consequently very small, the de- 
nominator tends to the limit 1. For h — u 2 /g, or « = V(g/»)> the 
denominator becomes zero. Hence, tabulating these results as 
before : — 

For h = 0, u 2 /g, > tt 2 /g, °° . 
the denominator becomes — 00, o, > o, 1. 

§ 118. Case 1. — Suppose h>u?/g, and also h>H, or the depth 
greater than that corresponding to uniform motion. In this case 
dh/ds is positive, and the stream increases in depth in the direction 
of flow. In fig. 122 let B0B1 be the bed, CcCi a line parallel to the 
bed and at a height above it equal to H. By hypothesis, the surface 




Fig. 122. 

A0A1 of the stream is above C0C1, and it has just been shown that the 
depth of the stream increases from Bo towards Bi. But going up 
stream h approaches more and more nearly the value H, and there- 
fore dh/ds approaches the limit o, or the surface of the stream is 
asymptotic to C0C1. Going down stream h increases and u diminishes, 
thenumeratorand denominator of thefraction(i — fw 2 _/2gi/j)/(l — u'jgh) 
both tend towards the limit I, and dh/ds to the limit i. That is, 
the surface of the stream tends to become asymptotic to a horizontal 
line D0D1. 

The form of water surface here discussed is produced when the 
flow of a stream originally uniform is altered by the construction of 
a weir. The raising of the water surface above the level C0C1 is 
termed the backwater due to the weir. 

§ 119. Case 2. — Suppose h>u l /g, and also h<H. Then dh/ds is 



7 6 



HYDRAULICS 



[FLOW IN RIVERS AND CANALS 




negative, and the stream is diminishing in depth in the direction of 
flow. In fig. 123 let BoB! be the stream bed as before; C0Q a line 
drawn parallel to B0B1 at a height above it equal to H. By hypo- 
thesis the surface A0A1 of the stream is below C0C1, and the depth has 

•just been shown to 
diminish from Bo 
towards Bi. Going 
up stream h ap- 
_Cj proaches the limit 
f H, and dh/ds tends 
to the limit zero. 
That is, up stream 
A0A1 is asymptotic 
to C0C1. Going down 
p IG j 2 -i ' stream h diminishes 

and u increases; the 
inequality h>u 2 ,'g diminishes; the denominator of the frac- 
tion (i—t;u 2 i2gih)l{i-u'lgk-) tends to the limit zero, and con- 
sequently dhjds tends to co . That is, down stream A0A1 tends 
to a direction perpendicular to the bed. Before, however, this 
limit was reached the assumptions on which the general equation is 
based would cease to be even approximately true, and the equation 
would cease_ to be applicable. The filaments would have a relative 
motion, which would make the influence of internal friction in the 
fluid too important to be neglected. A stream surface of this form 

may be pro- 
duced if there 
is an abrupt 
fall in the bed 
of the stream 
(fig. 124). 
On the Ganges 
canal, as orig- 
inally con- 
structed, there 
were abrupt 
falls precisely 
of this kind, 
and it appears 

that the lowering of the water surface and increase of velocity 
which such falls occasion, for a distance of some miles up stream, 
was not foreseen. The result was that, the velocity above the 
falls being greater than was intended, the bed was scoured and 
considerable damage was done to the works. " When the canal 
was first opened the water was allowed to pass freely over the 
crests of the overfalls, which were laid on the level of the bed 
of the earthen channel; erosion of bed and sides for some miles 
up rapidly followed, and it soon became apparent that means 
must be adopted for raising the surface of the stream at 
those points (that is, the crests of the falls). Planks were accord- 
ingly fixed in the grooves above the bridge arches, or temporary 
weirs were formed over which the water was allowed to fall ; in some 
cases the surface of the water was thus raised above its normal 
height, causing a backwater in the channel above " (Crofton's 
Report on the Ganges Canal, p. 14). Fig. 125 represents in an ex- 
aggerated form what probably occurred, the diagram being intended 




Fig. 124. 




Fig. 125. 

to represent some miles' length of the canal bed above the fall. 
AA parallel to the cana! bed is the level corresponding to uniform 
motion with the intended velocity of the canal. In consequence of 
the presence of the ogee fall, however, the water surface would take 
some such form as BB, corresponding to Case 2 above, and the 
velocity would be greater than the intended velocity, nearly in the 
inverse ratio of the actual to the intended depth. By constructing 
a weir on the crest of the fall, as shown by dotted lines, a new water 
surface CC corresponding to Case 1 would be produced, and by 
suitably choosing the height of the weir this might be made to agree 
approximately with the intended level AA. 

§ 120. Case 3. — Suppose a stream flowing uniformly with a depth 
h<u 2 /g. For a stream in uniform motion $u i J2g = mi, or if the 



stream is of indefinitely great width, so that m = H,then fw 2 /2g=iH, 
and H = fM 2 /2gi. Consequently the condition stated above involves 
that 

|w 2 /2g»'<M 2 /g, or that«>f/2. 
If such a stream is interfered with by the construction of a weir 
which raises its level, so that its depth at the weir becomes /fi>« 2 /g, 
then for a portion of the stream the depth h will satisfy the con- 
ditions h<u 2 /g and h>H, which are not the same as those assumed 
in the two previous cases. At some point of the stream above the 
weir the depth h becomes equal to u 2 /g, and at that point dh/ds 
becomes infinite, or the surface of the stream is normal to the bed. 
It is obvious that at that point the influence of internal friction will 
be too great to be neglected, and the general equation will cease to 
represent the true conditions of the motion of the water. It is known 
that, in cases such as this, there occurs an abrupt rise of the free 
surface of the stream, or a standing wave is formed, the conditions 
of motion in which will be examined presently. 

It appears that the condition necessary to give rise to a standing 
wave is that i>f/2. Now f depends for different channels on the 
roughness of the channel and its hydraulic mean depth. Bazin 
calculated the values of f for channels of different degrees of rough- 
ness and different depths given in the following table, and the corre- 
sponding minimum values of i for which the exceptional case of the 
production of a standing wave may occur. 





Slope below 
which a Stand- 


Standing Wave Formed. 










impossible in 


Slope in feet Least Depth 




feet per foot. 


per foot. 


in feet . 






("0-002 


0-262 


Very smooth cemented surface 


0-OOI47 


< 0-003 


•O98 






1.0-004 


•O65 






( O-O03 


•394 


Ashlar or brickwork . 


0-OOI86 


< 0-004 


• 197 






I 0-O06 


•098 






C 0-004 


■ 1-181 


Rubble masonry .... 


0-00235 


< 0-006 


•525 






lo-oio 


•262 






ro-oo6 


3-478 


Earth 


0-00275 


< 0-010 


1-542 






lo-OI5 


•919 



Standing Waves 

§ 121. The formation of a standing wave was first observed by 
Bidone. Into a small rectangular masonry channel, having a slope 
of 0-023 ft- per foot, he admitted water till it flowed uniformly with 
a depth of 0-2 ft. He then placed a plank across the stream which 
raised the level just above the obstruction to 0-95 ft. He found that 
the stream above the obstruction was sensibly unaffected up to a 
point 15 ft. from it. At that point the depth suddenly increased 
from 0-2 ft. to 0-56 ft. The velocity of the stream in the part un- 
affected by the obstruction was 5-54 ft. per second. Above the point 
where the abrupt change of depth occurred w 2 = 5-54 2 = 30-7, and 
gh = 32-2X0-2 =6-44; hence « 2 was>g&. Just below the abrupt 
change of depth « = 5-54Xo-2/o-56 = i-97; « 2 = 3-88; and gh = 
32-2X0-56 = 18-03; hence at this point u 2 <gh. Between these two 
points, therefore, u 2 = gk; and the condition for the production of a 
standing wave occurred. 

The change of level at a standing wave may be found thus. Let 
fig. 126 represent the longitudinal section of a stream and ab, cd 




cross sections normal to the bed, which for the short distance con- 
sidered may be assumed horizontal. Suppose the mass of water 
abed to come to a'b'c'd' in a short time /; and let Mo, «i be the 
velocities at ab and cd, fio, Sii the areas of the cross sections. The force 
causing change of momentum in the mass abed estimated horizont- 
ally is simply the difference of the pressures on ab and cd. Putting 
ht,, hi for the depths of the centres of gravity of ab and cd measured 
down from the free water surface, the force is G(M4> — h$li) pounds, 
and the impulse in t seconds is G (/zofio — h\Q{) t second pounds. 
The horizontal change of momentum is the difference of the momenta 
of ede'd' and aba'V ; that is, 

(G/g)(n 1 « 1 2 -n « 2 )^ 



ON STREAMS AND RIVERS] 



HYDRAULICS 



77 



Hence, equating impulse and change of momentum, 

G(WJo-Ai«i)' = (G/g)(att! 2 -SW)<; 
.-. hno-h,i2i = (UiUi 2 -^ku 2 )/g. (i) 

For simplicity let the section be rectangular, of breadth B and 
depths Ho and Hi, at the two cross sections considered; then 
ho = jHo, and hi = jHi. Hence 

H„ 2 -Hi 2 = (2/g)(Hi«i 2 -Ho«o 2 ). 
But, since f2e«o = Bi«i, we have 

Wi a = «oW/Hi s , 
■ H 2 -Hi 2 = (2M 2 /g)(H„ 2 /Hi-H„). (2) 

This equation is satisfied if H = Hi, which corresponds to the case 
of uniform motion. Dividing by Ho — Hi, the equation becomes 
(H I /H„)(H„+H,)=2«„ 2 /g; (3) 

.-. Hi = V(2«o 2 Ho/g+iI-Io 2 )-§Ho. (4) 

In Bidone's experiment 00 = 5-54, andH =o-2. Hence Hi=o-52, 
which agrees very well with the observed height. 

§ 122. A standing wave is frequently produced at the foot of 
a weir. Thus in the ogee falls originally constructed on the Ganges 
canal a standing wave was observed as shown in fig. 127. The water 
falling over the weir crest A acquired a very high velocity on the 





Cultivated land and spring- ) 
forming declivities . . \ 
Wooded hilly slopes . 
Naked unfissured mountains 



Ratio of average 

Discharge to 
average Rainfall. 



•3 to -33 
•35 to -45 
■55 to -6o 



Loss by Evaporation, 

&c, in percent of 

total Rainfall. 



67 to 70 

55 to 65 

40 to 45 



Fig. 127. 

steep slope AB, and the section of the stream at B became very 
small. It easily happened, therefore, that at B the depth h<u'/g. 
In flowing along the rough apron of the weir the velocity u diminished 
and the depth h increased At a point C, where h became equal to 
u'lg, the conditions for producing the standing wave occurred. 
Beyond C the free surface abruptly rose to the level corresponding to 
uniform motion with the assigned slope of the lower reach of the 
canal. 

A standing wave is sometimes formed on the down stream side of 
bridges the piers of which obstruct the flow of the water. Some 
interesting cases of this kind are described in a paper on the " Floods 
in the Nerbudda Valley " in the Proc. Inst. Civ. Eng. vol. xxvii. 
p. 222, by A. C. Howden. Fig. 128 is compiled from the data given 
in that paper. It represents the section of the stream at pier 8 of 

the Towah Viaduct, 
during the flood of 1865. 
The ground level is not 
exactly given by How- 
den, but has been in- 
ferred from data given 
on another drawing. The 
velocity of the stream 
was not observed, but 
the author states it was 
probably the same as at 
the Gunjal river during 
a similar flood, that is 
16-58 ft. per second. 
Now, taking the depth 
on the down stream face 
of the pier at 26 ft., the 
velocity necessary for the 
production of a standing 
wave would be u = V (gh) 
= V (32-2X26) =29 ft. 
per second nearly. But 
the velocity at this 
point was probably from Howden's statements 16-58x1? =25-5 
ft., an agreement as close as the approximate character of the 
data would lead us to expect. 

XI. ON STREAMS AND RIVERS 

§ 123. Catchment Basin. — A stream or river is the channel for the 
discharge of the available rainfall of a district, termed its catchment 
basin. The catchment basin is surrounded by a ridge or watershed 
line, continuous except at the point where the river finds an outlet. 
The area of the catchment basin may be determined from a suitable 
contoured map on a scale of at least 1 in 100,000. Of the whole rain- 
fall on the catchment basin, a part only finds its way to the stream. 
Part is directly re-evaporated, part is absorbed by vegetation, part 
may escape by percolation into neighbouring districts. The follow- 
ing table gives the relation of the average stream discharge to the 
average rainfall on the catchment basin (Tiefenbacher). 



§ 124. Flood Discharge. — The flood discharge can generally only be 
determined by examining the greatest height to which floods have 
been known to rise. To produce a flood the rainfall must be heavy 
and widely distributed, and to produce a flood of exceptional height 
the duration of the rainfall must be so g^eat that the flood waters 
of the most distant affluents reach the point considered, simultane- 
ously with those from nearer points. The larger the catchment 
basin the less probable is it that all the conditions tending to pro- 
duce a maximum discharge should simultaneously occur. Further, 
lakes and the river bed itself act as storage reservoirs during the rise 
of water level and diminish the rate of discharge, or serve as flood 
moderators. The influence of these is often important, because very 
heavy rain storms are in most countries of comparatively short 
duration. Tiefenbacher gives the following estimate of the flood 
discharge of streams in Europe : — - 

Flood discharge of Streams 

per Second per Square Mile 

of Catchment Basin. 

In flat country 8-7 to 12-5 cub. ft. 

In hilly districts 17-5 to 22-5 ,, 

In moderately mountainous districts 36-2 to 45-0 ,, 
In very mountainous districts . . 50-0 to 75-0 ,, 
It has been attempted to express the decrease of the rate of flood 
discharge with the increase of extent of the catchment basin by 
empirical formulae. Thus Colonel P. P. L. O'Connell proposed the 
formula j = MV*, where M is a constant called the modulus of the 
river, the value of which depends on the amount of rainfall, the 
physical characters of the basin, and the extent to which the floods 
are moderated by storage of the water. If M is small for any given 
river, it shows that the rainfall is small, or that the permeability or 
slope of the sides of the valley is such that the water does not drain 
rapidly to the river, or that lakes and river bed moderate the rise of 
the floods. If values of M are known for a number of rivers, they 
may be used in inferring the probable discharge of other similar rivers. 
For British rivers M varies from 0-43 for a small stteam draining 
meadow land to 37 for the Tyne. Generally it is about 15 or 20. 
For large European rivers M varies from 16 for the Seine to 67-5 for 
the Danube. For the Nile M = 1 1 , a low value which results from the 
immense length of the Nile throughout which it receives no affluent, 
and probably also from the influence of lakes. For different tribu- 
taries of the Mississippi M varies from 13 to 56. For various Indian 
rivers it varies from 40 to 303, this variation being due to the great 
variations of rainfall, slope and character of Indian rivers. 

In some of the tank projects in India, the flood discharge has been 
calculated from the formula D=C-v'w 2 , where D is the discharge in 
cubic yards per hour from n square miles of basin. The constant C 
was taken =61,523 in the designs for the Ekrooka tank, =75,000 on 
Ganges and Godavery works, and =10,000 on Madras works. 

§ 125. Action of a Stream on its Bed. — If the velocity of a stream 
exceeds a certain limit, depending on its size, and on the size, heavi- 
ness, form and coherence of the 
material of which its bed is com- 
posed, it scours its bed and 
carries forward the materials. 
The quantity of material which 
a given stream can carry in 
suspension depends on the size a 

and density of the particles in Fig. 129. 

suspension, and is greater as 
the velocity of the stream is greater, 
velocity of a stream is great enough 



If in one part of its course the 
to scour the bed and the water 
becomes loaded with silt, and in a subsequent part of the river's 
course the velocity is diminished, then part of the transported 
material must be deposited. Probably deposit and scour go on 
simultaneously over the whole river bed, but in some parts the rate 
of scour is in excess of 
the rate of deposit, and 
in other parts the rate 
of deposit is in excess 
of the rate of scour. 
Deep streams appear to 
have the greatest scour- 
ing power at any given 

velocity. It is possible «.'"' C' 

that the difference is p 

strictly a difference of • o • 

transporting, not of scouring action. Let fig. 129 represent a section of 

a stream. The material lifted at a will be diffused through the mass of 

the stream and deposited at different distances down stream. The 

average path of a particle lifted at a will be some such curve as abc, 

and the average distance of transport each time a particle is lifted 



78 



HYDRAULICS 



[ON STREAMS 



will be represented by ac. In a deeper stream such as that in fig. 
130, the average height to which particles are lifted, and, since the 
rate of vertical fall through the water may be assumed the same as 
before, the average distance a'c' of transport will be greater. Con- 
sequently, although the scouring action may be identical in the two 
streams, the velocity of transport of material down stream is greater 
as the depth of the stream is greater. The effect is that the deep 
stream excavates its bed more rapidly than the shallow stream. 

§ 126. Bottom Velocity at which Scour commences. — The following 
bottom velocities were determined by P. L. G. Dubuat to be the 
maximum velocities consistent with stability of the stream bed for 
different materials. 

Darcy and Bazin give, for the relation of the mean velocity v m 
and bottom velocity vt,. 

*ra=t'i4-iO'8/V (mi). 
But 

V»»t'=f m v(f/2g); 

.-. » m =»6/(l-IO-87V(r/2g)). 

Taking a mean value for f , we get 

t' m = I-3I2l>6, 

and from this the following values of the mean velocity are ob- 
tained : — 





Bottom Velocity 


Mean Velocity 

= V m . 


1. Soft earth 

2. Loam .... 

3. Sand .... 

4. Gravel 

5. Pebbles 

6. Broken stone, flint 

7. Chalk, soft shale 

8. Rock in beds . 

9. Hard rock 




0-25 
0-50 

I-OO 
2-0O 

3-40 
4-00 
5-00 
6-oo 

10-00 


•33 

•65 

i-3° 

2-62 

4-46 

5-25 

656 

7-87 

13-12 



The following table of velocities which should not be exceeded 
in channels is given in the Ingenieurs Taschenbuch of the Verein 
" Hiitte ": — 



Slimy earth or brown clay 

Clay 

Firm sand 

Pebbly bed 

Boulder bed . 

Conglomerate of slaty fragments 

Stratified rocks 

Hard rocks 



§ 127. Regime of a River Channel. — A river channel is said to be in 
a state of regime, or stability, when it changes little in draught or 
form in a series of years. In some rivers the deepest part of the 
channel changes its position perpetually, and is seldom found in the 
same place in two successive years. The sinuousness of the river 
also changes by the erosion of the banks, so that in time the position 
of the river is completely altered. In other rivers the change from 
year to year is very small, but probably the regime is never perfectly 
stable except where the rivers flow over a rocky bed. 

If a river had a constant discharge it would gradually modify its 
bed till a permanent regime was established 



9 

3 



it. Tijne 



3-Sff: 



— - ym-.-- 
If* 



Fig. 131 



discharged is constantly changing, and therefore 

the velocity, silt is deposited when the velocity 

decreases, and scour goes on when the velocity 

increases in the same place. When the scouring 

and silting are considerable, a perfect balance 

between the two is rarely established, and hence 

continual variations occur in the form of the river 

and the direction of its currents. In other cases, 

where the action is less violent , a tolerable balance may be established, 

and the deepening of the bed by scour at one time is compensated by 

the silting at another. In that case the general regime is permanent, 

though alteration is constantly going on. This is more likely to 



happen if by artificial means the erosion of the banks is prevented. 
If a river flows in soil incapable of resisting its tendency to scour 
it is necessarily sinuous (§ 107), for the slightest deflection of the 
current to either side begins an erosion which increases progres- 
sively till a considerable bend is formed. If such a river is 
straightened it becomes sinuous again unless its banks are pro- 
tected from scour. 

§ 128. Longitudinal Section of River Bed. — The declivity of rivers 
decreases from source to mouth. In their higher parts rapid and 
torrential, flowing over beds of gravel or boulders, they enlarge in 
volume by receiving affluent streams, their slope diminishes, their 
bed consists of smaller materials, and finally they reach the sea. 
Fig. 131 shows the length in miles, and the surface fall in feet per 
mile, of the Tyne and its tributaries. 

The decrease of the slope is due to two causes. (1) The action of 
the transporting power of the water, carrying the smallest debris 
the greatest distance, causes the bed to be less stable near the mouth 
than in the higher parts of the river; and, as the river adjusts its 
slope to the stability of the bed by scouring or increasing its sinuous- 
ness when the slope is too great, and by silting or straightening its 
course if the slope is too small, the decreasing stability of the bed 
would coincide with a decreasing slope. (2) The increase of volume 
and section of the river leads to a decrease of slope; for the larger 
the section the less slope is necessary to ensure a given velocity. 

The following investigation, though it relates to a purely arbitrary 
case, is not without interest. Let it be assumed, to make the con- 
ditions definite — (1) that a river flows over a bed of uniform resist- 
ance to scour, and let it be further assumed that to maintain stability 
the velocity of the river in these circumstances is constant from 
source to mouth; (2) suppose the sections of the river at all points 
are similar, so that, b being the breadth of the river at any point, its 
hydraulic mean depth is ab and its section is cb"-, where a and c are 
constants applicable to all parts of the river; (3) let us further assume 
that the discharge increases uniformly in consequence of the supply 
from affluents, so that, if I is the length of the river from its source to 
any given point, the 

discharge there will be ^ jy % 

kl, where k is another — 
constant applicable to 
all points in the course 
of the river. 

Let AB (fig. 132) be 
the longitudinal section 
of the river, whose 
source is at A; and 
take A for the origin of 

vertical and horizontal coordinates. Let C be a point whose ordinates 
are x and y, and let the river at C have the breadth b, the slope i, 
and the velocity v. 

Since velocity X area of section = discharge, vcb 2 = kl, or i = V (kl/cv). 
Hydraulic mean depth — ab = a-4 (kl/cv). 
But, by the ordinary formula for the flow of rivers, mi — ty 1 ; 

:. i = tv 2 /m = (i'vVa)^ (c/kl). 
But i is the tangent of the angle which the curve at C makes with 
the axis of X, and is therefore = dy/dx. Also, as the slope is small, 
I = AC = AD =x nearly. 

.". dy/dx - (jti"/o) V (c/kx) ; 
and, remembering that v is constant, 

y = (2f»l/o)V(c*/*); 
or y 2 = constant X x ; 

so that the curve is a common parabola, of which the axis is hori- 
But as the volume zontal and the vertex at the source. This may be considered an 

ideal longitudinal section, to which actual rivers ap- 
proximate more or less, with exceptions due to the vary- 
ing hardness of their beds, and the irregular manner in 
which their volume increases. 

§ 129. Surface Level of River. — The surface level of a 
river is a plane changing constantly in position from 
changes in the volume of water discharged, and more 
slowly from changes in the river bed, and the circum- 
stances affecting the drainage into the river. 

For the purposes 01 the engineer, it is important to 
determine (1) the extreme low water level, (2) the 
extreme high water or flood level, and (3) the highest 
navigable level. 

I. Low Water Level cannot be absolutely known, 
because a river reaches its lowest level only at rare inter- 
vals, and because alterations in the cultivation of the 
land, the drainage, tne removal of forests, the removal 
or erection of obstructions in the river bed, &c, gradu- 
ally alter the conditions of discharge. The lowest level 
of which records can be found is taken as the conven- 
tional or approximate low water level, and allowance is 
made for possible changes. 
2. High Water or Flood Level. — The engineer assumes as the highest 
flood level the highest level of which records can be obtained. In 
forming a judgment of the data available, it must be remembered that 
the highest level at one point of a river is not always simultaneous 



Surface 


Mean 


Bottom 


Velocity. 


Velocity. 


Velocity. 


•49 


•36 


•26 


•98 


•75 


•52 


1-97 


i-5i 


1-02 


4-00 


3-15 


2-30 


5-00 


4-o3 


3-o8 


7-28 


6-io 


4-90 


8-oo 


7-45 


6-oo 


14-00 


12-15 


10-36 





AND RIVERS] 



HYDRAULICS 



79 



with the attainment of the highest level at other points., and that 
the rise of a river in flood is very different in different parts of its 
course. In temperate regions, the floods of rivers seldom rise more 
than 20 ft. above low-water level, but in the tropics the rise of floods 
is greater. 

3. Highest Navigable Level. — When the river rises above a certain 
level, navigation becomes difficult from the increase of the velocity 
of the current, or from submersion of the tow paths, or from the head- 
way under bridges becoming insufficient. Ordinarily the highest 
navigable level may be taken to be that at which the river begins to 
overflow its banks. 

§ 130. Relative Value of Different. Materials for Submerged Works. — 
That the power of water to remove and transport different materials 
depends on their density has an important bearing on the selection 
of materials for submerged works. In many cases, as in the aprons 
or floorings beneath bridges, or in front of locks or falls, and in the 
formation of training walls and breakwaters by pierres perdus, 
which have to resist a violent current, the materials of which the 
structures are composed should be of such a size and weight as to 
be able individually to resist the scouring action of the water. The 
heaviest materials will therefore be the best; and the different value 
of materials in this respect will appear much more striking, if it is 
remembered that all materials lose part of their weight in water. 
A block whose volume is V cubic feet, and whose density in air is 
w lb per cubic foot, weighs in air w\ lb, but in water only (w — 62-4.) 
V ft. 





Weight of a. Cub. Ft. in lb. 


In Air. 


In Water. 


Basalt 

Brick 

Brickwork .... 
Granite and limestone 
Sandstone 
Masonry .... 


187-3 
130-0 

II2-0 
I70-0 

144-0 
116-144 


124-9 

67-6 

49-6 

107-6 

8i-6 

53-6-81-6 



river, and chained and levelled. The cross sections are referred to 
the line of stakes, both as to position and direction. The determina- 
tion of the surface slope is very difficult, partly from its extreme 
smallness, partly from oscillation of the water. Cunningham recom- 
mends that the slope be taken in a length of 2000 ft. by four simul- 
taneous observations, two on each side of the river. 

§ 134. Cross Sections — A stake is planted flush with the water, and 
its level relatively to some point on the line of levels is determined. 
Then the depth of the water is determined at a series of points (if 



§ 131. Inundation Deposits from a River. — When a river carrying 
silt periodically overflows its banks, it deposits silt over the area 
flooded, and gradually raises the surface of the country. The silt is 
deposited in greatest abundance where the water first leaves the 
river. It hence results that the section of the country assumes a 
peculiar form, the river flowing in a trough along the crest of a ridge, 
from which the land slopes downwards on both sides. The silt 
deposited from the water forms two wedges, having their thick ends 
towards the river (fig. 133). 



Fig. 133. 

This is strikingly the case with the Mississippi, and that river is 
now kept from flooding immense areas by artificial embankments or 
levees. In India, the term deltaic segment is sometimes applied to 
that portion of a river running through deposits formed by inunda- 
tion, and having this characteristic section. The irrigation of the 
country in this case is very easy; a comparatively slight raising of 
the river surface by a weir or annicut gives a command of level 
which permits the water to be conveyed to any part of the district. 

§ 132. Deltas. — The name delta was originally given to the A- 
shaped portion of Lower Egypt, included between seven branches of 
the Nile. It is now given to the whole of the alluvial tracts round 
river mouths formed by deposition of sediment from the river, where 
its velocity is checked on its entrance to the sea. The characteristic 
feature of these alluvial deltas is that the river traverses them, not 
in a single channel, but in two or many bifurcating branches. Each 
branch has a tract of the delta under its influence, and gradually 
raises the surface of that tract, and extends it seaward. As the delta 
extends itself seaward, the conditions of discharge through the 
different branches change. The water. finds the passage through 
one of the branches less obstructed than through the others; the 
velocity and scouring action in that branch are increased ; in the 
others they diminish. The one channel gradually absorbs the whole 
of the water supply, while the other branches silt up. But as the 
mouth of the new main channel extends seaward the resistance in- 
creases both from the greater length of the channel and the formation 
of shoals at its mouth, and the river tends to form new bifurcations 
AC or AD (fig. 134), and one of these may in time become the main 
channel of the river. 

§ 133. Field Operations preliminary to a Study of River Improve- 
ment. — There are required (1) a plan of the river, on which the 
positions of lines of levelling and cross sections are marked; (2) a 
longitudinal section and numerous cross sections of the river; (3) a 
series of gaugings of the discharge at different points and in different 
conditions of the river. 

Longitudinal Section. — This requires to be carried out with great 
accuracy. A line of stakes is planted, following the sinuosities of the 




Fig. 134. 

possible at uniform distances) in a line starting from the stake and 
perpendicular to the thread of the stream. To obtain these, a wire 
may be stretched across with equal distances marked on it by hang- 
ing tags. The depth at each of these tags may be obtained by a 
light wooden staff, with a disk-shaped shoe 4 to 6 in. in diameter. 
If the depth is great, soundings may be taken by a chain and weight. 
To ensure the wire being perpendicular to the thread of the stream, 
it is desirable to stretch two other wires similarly graduated, one 
above and the other below, at a distance of 20 to 40 yds. A 
number of floats being then thrown in, it is observed whether they 
pass the same graduation on each wire. 

For large and rapid rivers the cross section is obtained by sounding 
in the following way. Let AC (fig. 135) be the line on which sound- 
ings are required. A base line AB is measured out at right angles 
to AC, and ranging staves are set up at AB and at D in line with AC. 
A boat is allowed to drop down stream, and, at the moment it comes 
in line with AD, the lead is 
dropped, and an observer in the 

boat takes, with a box sextant, £ 

the angle AEB subtended by 
AB. The sounding line may 
have a weight of 14 lb of lead, 
and, if the boat drops down 
stream slowly, it may hang near 
the bottom, so that the observa- 
tion is made instantly. In ex- 
tensive surveys of the Missis- 
sippi observers with theodolites 
were stationed at A and B. The 1 I 

theodolite at A was directed 
towards C, that at B was kept 
on the boat. When the boat 
came on the line AC, the ob- 
server at A signalled, the sound- 
ing line was dropped, and the Fig. 135. 
observer at B read off the angle 
ABE. By repeating observations a number of soundings are ob- 
tained, which can be plotted in their proper position, and the form 
of the river bed drawn by connecting the extremities of the lines. 
From the section can be measured the sectional area of the stream 
SI and its wetted perimeter x; and from these the hydraulic mean 
depth m can be calculated. 

§ 135. Measurement of the Discharge of Rivers. — The area of cross 
section multiplied by the mean velocity gives the discharge of the 
stream. The height of the river with reference to some fixed mark 
should be noted whenever the velocity is observed, as the velocity 
and area of cross section are different in differest states of the river. 
To determine the mean velocity various methods may be adopted; 
and, since no method is free from liability to error, either from the 
difficulty of the observations or from uncertainty as to the ratio of 
the mean velocity to the velocity observed, it is desirable that more 
than one method should be used. 

Instruments for Measuring the Velocity of Water 

§ 136. Surface Floats are convenient for determining the surface 
velocities of a stream, though their use is difficult near the banks. 
The floats may be small balls of wood, of wax or of hollow metal, so 
loaded as to float nearly flush with the water surface. To render 



6 
B 



8o 



HYDRAULICS 



[ON STREAMS 



A 

9- 



B 



ii 

ll 


r 




!i 


il 


i 

/ 
i 






i 


i 


* 




\v 




« 


I 


II 

! 


X 

\ 
\ 

\ 


1 ' 




! 


\ ** 




1:1 



.4' 



them visible they may have a vertical painted stem. In experi- 
ments on the Seine, cork balls if in. diameter were used, loaded to 
float flush with the water, and provided with a stem. In A. J. C. 
Cunningham's observations at Roorkee, the floats were thin circular 
disks of English deal, 3 in. diameter and \ in. thick. For observa- 
tions near the banks, floats 1 in. diameter and \ in. thick were used. 
To render them visible a tuft of cotton wool was used loosely hxed 
in a hole at the centre. 

The velocity is obtained by allowing the float to be carried down, 
and noting the time of passage over a measured length of the stream. 
If 11 is the velocity of any float, I the time of passing over a length 
/, then v = l/t. To mark out distinctly the length of stream over 
which the floats pass, two ropes may be stretched across the stream 
at a distance apart, which varies usually from 50 to25oft., according 
to the size and rapidity of the river. In the Roorkee experiments 
a length of run of 50 ft. was found best for the central two- fifths of the 
width, and 25 ft. for the remainder, except very close to the banks, 
where the run was made 12J ft. only. The longer the run the less 
is the proportionate error of the time observations, but on the other 
hand the greater the deviation of the floats from a straight course 
parallel to the axis of the stream. To mark the precise position at 
which the floats cross the ropes, Cunningham used short white rope 
pendants, hanging so as nearly to touch the surface of the water. In 
this case the streams were 80 to 180 ft. in width. In wider streams the 
use of ropes to mark the length of run is impossible, and recourse must 
be had to box sextants or theodolites to mark the path of the floats. 

Let AB (fig. 136) be a measured base line strictly parallel to the 
thread of the stream, and AAi, BBi lines at right angles to AB 
marked out by ranging rods at Ai and 
Bi. Suppose observers stationed at A 
and B with sextants or theodolites, and 
let CD be the path of any float down 
stream. As the float approaches AAi, 
the observer at B keeps it on the cross wire 
of his instrument. The observer at A 
observes the instant of the float reaching 
the line AAi, and signals to B who then 
reads off the angle ABC. Similarly, as 
the float approaches BBi, the observer 
at A keeps it in sight, and when signalled 
to by B reads the angle BAD. The data 
so obtained are sufficient for plotting 
the path of the float and determining 
the distances AC, BD. 

The time taken by the float in passing 
over the measured distance may be ob- 
served by a chronograph, started as the 
float passes the upper rope or line, and 
stopped when it passes the lower. In 
Cunningham's observations two chrono- 
meters were sometimes used, the time of passing one end of the run 
being noted on one, and that of passing the other end of the run 
being noted on the other. The chronometers were compared 
immediately before the observations. In other cases a single 
chronometer was used placed midway of the run. The moment of 
the floats passing the ends of the run was signalled to a time- 
keeper at the chronometer by shouting. It was found quite pos- 
sible to count the chronometer beats to the nearest half second, 
and in some cases to the nearest quarter second. 

§ 137. Sub-surface Floats. — The velocity at different depths below 
the surface of a stream may be obtained by sub-surface floats, used 
precisely in the same way as surface floats. The most usual arrange- 
ment is to have a large float, of slightly greater density than water, 
connected with a small and very light surface float. The motion 
of the combined arrangement is not 
sensibly different from that of the large 
float, and the small surface float enables 
an observer to note the path and velo- 
city of the sub-surface float. The in- 
strument is, however, not free from 
objection. If the large submerged 
float is made of very nearly the same 
density as water, then it is liable to be 
thrown upwards by very slight eddies 
in the water, and it does not maintain 
its position at the depth at which it is 
intended to float. On the other hand, 
if the large float is made sensibly 
heavier than water, the indicating or 
surface float must be made rather large, 
and then it to seme extent influences 
the motion of the submerged float. 
Fig. 137 shows one form of sub- 
surface float. It consists of a couple 
of tin plates bent at a right angle and soldered together at the angle. 
This is connected with a wooden ball at the surface by a very thin 
wire or cord. As the tin alone makes a heavy submerged float, it is 
better to attach to the tin float some pieces of wood to diminish its 
weight in water. Fig. 138 shows the form of submerged float used 



by Cunningham. It consists of a hollow metal ball connected to a 
slice of cork, which serves as the surface float. 

§ 138. Twin Floats. — Suppose two equal and similar floats (fig. 139) 
connected by a wire. Let one float be a little lighter and the other 
a little heavier than water. Then the velocity of the combined 






Fig. 136. 






Fig. 138. 



Fig. 139. 



Fig. 137. 



floats will be the mean of the surface velocity and the velocity at the 
depth at which the heavier float swims, which is determined by the 
length of the connecting wire. Thus if v, is the surface velocity 
and v d the velocity at the depth to which the lower float is sunk, the 
velocity of the combined floats will be 

v = i(v s +v d ). 
Consequently, if v is observed, and v, determined by an experiment 
with a single float, 

Vd = 2V—V„ 

According to Cunningham, the twin float gives better results than 

the sub-surface float. 

§ 139. Velocity Rods. — Another form of float is shown in fig. 140. 

This consists of a cylindrical rod loaded at the lower end so as to 

float nearly vertical in water. A wooden rod, with a metal cap at the 

bottom in which shot can be placed, 

answers better than anything else, and 

sometimes the wooden rod is made in 

lengths, which can be screwed together 

so as to suit streams of different depths. 

A tuft of cotton wool at the top serves 

to make the float more easily visible. 

Such a rod, so adjusted in length that it 

sinks nearly to the bed of the stream, 

gives directly the mean velocity of the 

whole vertical section in which it floats. 

§ 140. Revy's Current Meter. — No in- 
strument has been so much used in 

directly determining the velocity of a 

stream at a given point as the screw 

current meter. Of this there are a 

dozen varieties at least. As an example 

of the instrument in its simplest form, 
Revy's meter may be selected. This is an 

ordinary screw meter of a larger size than 

usual, more carefully made, and with its I 

details carefully studied (figs. 141, 142). 
It was designed after experience in gaug- 
ing the great South American rivers. The screw, which is actuated by 
the water, is 6 in. in diameter, and is of the type of the Griffiths screw 
used in ships. The hollow spherical boss serves to make the weight of 
the screw sensibly equal to its displacement, so that friction is much 
reduced. On the axis aa of the screw is a worm which drives the 
counter. This consists of two worm wheels g and h fixed on a common 
axis. The worm wheels are carried on a frame attached to the pin I. 
By means of a string attached to / they can be pulled into gear with 
the worm, or dropped out of gear and stopped at any instant. A 
nut m can be screwed up, if necessary, to keep the counter per- 
manently in gear. The worm is two-threaded, and the worm wheel 
g has 200 teeth. Consequently it makes one rotation for 100 rota- 
tions of the screw, and the number of rotations up to 100 is marked 
by the passage of the graduations on its edge in front of a fixed index. 
The second worm wheel has 196 teeth, and its edge is divided into 
49 divisions. Hence it falls behind the first wheel one division for a 
complete rotation of the latter. The number of hundreds of rota- 
tions of the screw are therefore shown by the number of divisions on 
h passed over by an index fixed to g. One difficulty in the use of the 
ordinary screw meter is that particles of grit, getting into the working 
parts, very sensibly alter the friction, and therefore the speed of the 
meter. Revy obviates this by enclosing the counter in a brass box 
with a glass face. This box is filled with pure water, which ensures a 
constant coefficient of friction for the rubbing parts, and prevents any 
mud or grit finding its way in. In order that the meter may place itself 
with the axis parallel to the current, it is pivoted on a vertical axis 
and directed by a large vane shown in fig. 142. To give the vane 




Fig. 140. 



AND RIVERS] 



HYDRAULICS 



81 



more directing power the vertical axis is nearer the screw than in 
ordinary meters, and the vane is larger. A second horizontal vane is 
attached by the screws x, x, the object of which is to allow the meter 
to rest on the ground without the motion of the screw being inter- 
fered with. The string or wire for starting and stopping the meter is 




counter has to be held in gear. For deep streams the meter A is 
suspended by a wire with a heavy lenticular weight below (fig. 144). 
The wire is payed out from a small winch D, with an index showing 
the depth of the meter, and passes over a pulley B. The meter is in 
gimbals and is directed by a conical rudder which keeps it facing the 
stream with its axis horizontal. There is an electric circuit from a 
battery C through the meter, and a contact is made closing the circuit 
every 100 revolutions. The moment the circuit closes a bell rings. 
By a subsidiary arrangement, when the foot of the instrument, 0-3 
metres below the axis of the meter, touches the ground the circuit is 
also closed and the bell rings. It is easy to distinguish the continuous 
ring when the ground is reached from the short ring when the counter 
signals. A convenient winch for the wire is so graduated that if 



Fig. 141. 
carried through the centre of the vertical axis, so that the strain on 
it may not tend to pull the meter oblique to the current. The pitch 
of the screw is about 9 in. The screws at x serve for filling the meter 
with water. The whole apparatus is fixed to a rod (fig. 142), of a 
length proportionate to the depth, or for very great depths it is 
fixed to a weighted bar lowered by ropes, a plan invented by Revy. 
The instrument is generally used thus. The reading of the counter is 
noted, and it is put out of gear. The meter is 
then lowered into the water to the required 
position from a platform between two boats, 
or better from a temporary bridge. Then the 
counter is put into gear for one, two or five 
minutes. Lastly, the instrument is raised 
and the counter again read. The velocity is 
deduced from the number of rotations in unit 
time by the formulae given below. For 
surface velocities the counter may be kept 
permanently in gear, the screw being started 
and stopped by hand. 

§ 141. The Harlacher Current Meter. — In 
this the ordinary counting apparatus is aban- 
doned. A worm drives a worm wheel, which 
makes an electrical contact once for each 100 
rotations of the worm. This contact gives a 
signal above water. With this arrangement, 
a series of velocity observations can be made, 
without removing the instrument from the 
water, and a number of practical difficulties 
attending the accurate starting and stopping 
of the ordinary counter are entirely got rid 
of. Fig. 143 shows the meter. The worm 
wheel z makes one rotation for 100 of the 
screw. A pin moving the lever x makes the 
electrical contact. The wires b, c are led 
through a gas pipe B ; this also serves to 
adjust the meter to any required position on 
the wooden rod dd. The rudder or vane is 
shown at WH. The galvanic current acts on 
the electromagnet m, which is fixed in a 
small metal box containing also the battery. 
The magnet exposes and withdraws a coloured 
disk at an opening in the cover of the box. 

§ 142. Amsler Laffon Current Meter. — A 
very convenient and accurate current meter 
is constructed by Amsler Laffon of Schaff- 
hausen. This can be used on a rod, and 
put into and out of gear by a ratchet. The 
peculiarity in this case is that there is a double ratchet, so that 
one pull on the string puts the counter into gear and a second 
puts it out of gear. The string may be slack during the action 
of the meter, and there is less uncertainty than when the 




Fig. 142. 




Fig. 143. 



set when the axis of the meter is at the water surface it indicates at 
any moment the depth of the meter below the surface. Fig. 144 
shows the meter as used on a boat. It is a very convenient instru- 
ment for obtaining the velocity at different depths and can also be 
used as a sounding instrument. 

§ 143. Determination of the Coefficients of the Current Meter. — Sup- 
pose a series of observations has been made by towing the meter in 
still water at different speeds, and that it is required to ascertain from 
these the constants of the meter. If v is the velocity of the water and 
n the observed number of rotations per second, let 

. v=a+0n (1) 

where a and /3 are constants. Now let the meter be towed over a 
measured distance L, and let N be the revolutions of the meter and 
t the time of transit. Then the speed of the meter relatively 10 the 
water is L/t = v feet per second, and the number of revolutions per 
second is N/t = n. Suppose m observations have been made in this 
way, furnishing corresponding values of v and ra, the speed in each 
trial being as uniform as possible, 

2» = »l+«2+ . . . 
2D=fl+t>2+ ■ ■ ■ 

2nv = niVi+n 2 V2+ . . . 
2« s = n;+«i+ . . . 

[2»] 2 = [»l+»2+ . . .f 



82 



HYDRAULICS 



[ON STREAMS 



Then for the determination of the constants a and /3 in (l), by the 
method of least squares — 

_2m 2 Sz> — S«Zra» 
a ~ mXn 2 -[Xnf ' 

m'Snv — TvTn 
P ~~ niZn* - [2w] 2 - 
In a few cases the constants for screw current meters have been 
determined by towing them in R. E. Froude's experimental tank in 




Fig. 144. 

which the resistance of ship models is ascertained. In that case the 
data are found with exceptional accuracy. 

§ 144. Darcy Gauge or modified Pilot Tube. — A very old instru- 
ment for measuring velocities, invented by Henri Pitot in 1730 
(Histoire de I'Acadcmie des Sciences, 1732, p. 376), consisted simply 
of a vertical glass tube with a right-angled bend, placed so that its 
mouth was normal to the direction of flow (fig. 145). 

The impact of the stream on the mouth of the tube balances a 
column in the tube, the height of which is approximately h = v 2 J2g, 

where v is the velocity 
|p] f-j ij — 11 at the depth x. Placed 

L '' ' with its mouth parallel 

to the stream the water 
inside the tube is nearly 
at the same level as the 
surface of the stream, 
and turned with the 
mouth down stream, the 
fluid sinks a depth 
/i'=» 2 /2g nearly, though 
the tube in that case 
interferes with the free 
flow of the liquid and 
somewhat modifies the 
result. Pitot expanded 
the mouth of the tube so as to form a funnel or bell mouth. In that 
case he found by experiment 

h = i-sv-/2g. 
But there is more disturbance of the stream. Darcy preferred to 
mak« the mouth of the tube very small to avoid interference with the 





stream and to check oscillations of the water column. Let the 
difference of level of a pair of tubes A and B (fig. 145) be taken to be 
h = kv 2 /2g, then k may be taken to be a corrective coefficient whose 
value in well-shaped instruments is very nearly unity. By placing 
his instrument in front of a boat towed through water Darcy found 
k = 1 -034 ; by placing the instrument in a stream the velocity of 
which had been ascertained by floats, he found k = 1 -006 ; by readings 
taken in different parts of the section of a canal in which a known 
volume of water was flowing, he found k =0-993. He believed the 

first value to be too high in con- 
sequence of the disturbance caused 
by the boat. The mean of the other 
two values is almost exactly unity 
{Recherches hydrauliques, Darcy and 
Bazin, 1865, p. 63). W. B. Gregory 
used somewhat differently formed 
Pitot tubes for which the k = 1 (Am. 
Soc. Mech. Eng., 1903, 25). T. E. 
Stanton used a Pitot tube in deter- 
mining the velocity of an air current, 
and for his instrument he found 
£ = 1-030 to £ = 1-032 (" On the Re- 
sistance of Plane Surfaces in a 
Current of Air," Proc. Inst. Civ. 
Eng., 1904, 156). 

One objection to the Pitot tube 
in its original form was the great 
difficulty and inconvenience of 
reading the height h in the imme- 
diate neighbourhood of the stream 
surface. This is obviated in the 
Darcy gauge, which can be removed 
from the stream to be read. 

Fig. 146 shows a Darcy gauge. 
It consists of two Pitot tubes 
having their mouths at right angles. 
In the instrument shown, the two 
tubes, formed of copper in the 
lower part, are united into one for 
strength, and the mouths of the 
tubes open vertically and horizon- 
tally. The upper part of the tubes 
is of glass, and they are provided 
with a brass scale and two verniers 
b, b. The whole instrument is sup- 
ported on a vertical rod or small pile 
AA, the fixing at B permitting the 
instrument to be adjusted to any 
height on the rod, and at the same 
time allowing free rotation, so that 
it can be held parallel to the current. 
At c is a two-way cock, which can 
be opened or closed by cords. If 
this is shut, the instrument can be 
lifted out of the stream for reading. 
The glass tubes are connected at 
top by a brass fixing, with a stop 
cock a, and a flexible tube and 
mouthpiece m. The use of this is 
as follows. If the velocity is re- 
quired at a point near the surface of the stream, one at least of 
the water columns would be below the level at which it could be 
read. It would be in the copper part of the instrument. Suppose 
then a little air is sucked out by the tube m, and the cock a 
closed, the two columns will be forced up an amount correspond- 
ing to the difference between atmospheric pressure and that in the 
tubes. But the difference of level will remain unaltered. 

When the velocities to be measured are not very small, this instru- 
ment is an admirable one. It requires observation only of a single 
linear quantity, and does not require any time observation. The 
law connecting the velocity and the observed height is a rational 
one, and it is not absolutely necessary to make any experiments on 
the coefficient of the instrument. If we take i> = £V(2gft), then it 
appears from Darcy's experiments that for a well-formed instrument 
k does not sensibly differ from unity. Jt gives the velocity at a 
definite point in the stream. The chief difficulty arises from the fact 
that at any given point in a stream the velocity is not absolutely 
constant, but varies a little from moment to moment. Darcy in 
some of his experiments took several readings, and deduced the 
velocity from the mean of the highest and lowest. 

§ 145. Perrodil Hydrodynamometer. — This consists of a frame 
abed (fig. 147) placed vertically in the stream, and of a height not 
less than the stream's depth. The two vertical members of this 
frame are connected by cross bars, and united above water by a 
circular bar, situated in the vertical plane and carrying a horizontai 1 
graduated circle ef. This whole system is movable round its axis, 
being suspended on a pivot at g connected with the fixed support 
mn. Other horizontal arms serve as guides. The central vertical 
rod gr forms a torsion rod, being fixed at r to the frame abed, and, 
passing freely upwards through the guides, it carries a horizontal 



AND RIVERS] 



HYDRAULICS 



»3 



needle moving over the graduated circle ef. The support g, which 
carries the apparatus, also receives in a tubular guide the end of the 
torsion rod gr and a set screw for fixing the upper end of the torsion 
rod when necessary. The impulse of the stream of water is received 
on a circular disk *, in the plane of the torsion rod and the frame 
abed. To raise and lower the apparatus easily, it is not fixed directly 
to the rod mn, but to a tube kl sliding on mn. 

■Suppose the apparatus arranged so that the disk x is at that level 
*he stream where the velocity is to be determined. The plane 




Fig. 146. 

abed is placed parallel to the direction of motion of the water. Then 
the disk * (acting as a rudder) will place itself parallel to the stream 
on the down stream side of the frame. The torsion rod will be un- 
strained, and the needle will be at zero on the graduated circle. 
If, then, the instrument is turned by pressing the needle, till the plane 
abed of the disk and the zero of the graduated circle is at right angles 
to the stream, the torsion rod will be twisted through an angle which 
measures the normal impulse of the stream on the disk x. That angle 



will be given by the distance of the needle from zero. Observation 
shows that the velocity of the water at a given point is not constant. 
It varies between limits more or less wide. When the apparatus is 
nearly in its right position, the set screw at g is made to clamp the 
torsion spring. Then the needle is fixed, and the apparatus carrying 
the graduated circle oscillates. It 
is not, then, difficult to note the 
mean angle marked by the needle. 
Let r be the radius of the torsion 
rod, / its length from the needle 
over ef to r, and a the observed 
torsion angle. Then the moment 
of the couple due to the molecular 
forces in the torsion rod is 

M=EJo/Z; 
where E ( is the modulus of elas- 
ticity for torsion, and I the polar 
moment of inertia of the section of 
the rod. If the rod is of circular 
section, I=Jirr 4 . Let R be the 
radius of the disk, and b its 
leverage, or the distance of its 
centre from the axis of the torsion 
rod. The moment of the pressure 
of the water on the disk is 

Fb = kb(Gl2g)vRV, 
where G is the heaviness of water 
and k an experimental coefficient. 
Then 

E ( Io// = *6(G/2g)irRV. 
For any given instrument, 

w = cV a, 
where c is a constant coefficient for 
the instrument. _ 

The instrument as constructed had three disks which could be 
used at will. Their radii and leverages were in feet 




Fig. 147. n\ 





R = 


6 = 


1st disk 


. . 0-052 


0-16 


2nd „ 


. . 0-105 


0-32 


3rd „ 


. 0-2IO 


o-66 



For a thin circular plate, the coefficient k = i-i2. In the actual 
instrument the torsion rod was a brass wire 0-06 in. diameter and 
6| ft. long. Supposing a measured in degrees, we get by calculation 
V = 0-335^Ja; 0-II5Va; 0-042V<*. 

Very careful experiments were made with the instrument. It 

was fixed to a wooden turning bridge, revolving over a circular 

channel of 2 ft. width, and about 76 ft 'circumferential length. An 

allowance was made for the slight current produced in the channel. 

These experiments gave for the coefficient c, in the f ormula v = cV a, 

1st disk, c =0-3126 for velocities of 3 to 16 ft. 

2nd ,, 0-1177 ., .. iito3} ,, 

3rd „ 0-0349 .. » less than ij 

The instrument is preferable to the current meter in giving the 
velocity in terms of a single observed quantity, the angle of torsion, 
while the current meter involves the observation of two quantities, 
the number of rotations and the time. The current meter, except 
in some improved forms, must be withdrawn from the water to read 
the result of each experiment, and the law connecting the velocity 
and number of rotations of a current meter is less well-determined 
than that connecting the pressure on a disk and the torsion of the 
wire of a hydrodynamometer. 

_ The Pitot tube, like the hydrodynamometer, does not require a 
time observation. But, where the velocity is a varying one, and 
consequently the columns of water in the Pitot tube are oscillating, 
there is room for doubt as to whether, at any given moment of closing 
the cock, the difference of level exactly measures the impulse of 
the stream at the moment. The Pitot tube also fails to give measur- 
able indications of very low velocities. 

Processes for Gauging Streams 

§ 146. Gauging by Observation of the Maximum. Surface Velocity. — 
The method of gauging which involves the least trouble is to deter- 
mine the surface velocity at the thread of the stream, and to deduce 
from it the mean velocity of the whole cross section. The maximum 
surface velocity may be determined by floats or by a current meter. 
Unfortunately the ratio of the maximum surface to the mean velo- 
city is extremely variable. Thus putting v„ for the surface velocity 
at the thread of the stream, and v m for the mean velocity of the whole 
cross section, v m /v has been found to have the following values: — 

V m /Vo 

De Prony, experiments on small wooden channels 0-8164 

Experiments on the Seine 0-62 

Destrem and De Prony, experiments on the Neva 0-78 

Boileau, experiments on canals 0-82 

Baumgartner, experiments on the Garonne . . o-8o 

Brunings (mean) 0-85 

Cunningham, Solani aqueduct 0-823 



8 4 



HYDRAULICS 



[ON STREAMS AND RIVERS 



Various formulae, either empirical or based on some theory of the 
vertical and horizontal velocity curves, have been proposed for 
determining the ratio v m jv . Bazin found from his experiments the 
empirical expression 

"Om = Vo — 25 -4V {mi) ; 
where m is the hydraulic mean depth and i the slope of the stream. 
In the case of irrigation canals and rivers, it is often important to 
determine the discharge either daily or at other intervals of time, 
while the depth and consequently the mean velocity is varying. 
Cunningham {Roorkee Prof. Papers, iv. 47), has shown that, 
for a given part of such- a stream, where the bed is regular and of 
permanent section, a simple formula may be found for the variation 
of the central surface velocity with the depth. When once the 
constants of this formula have been determined by measuring the 
central surface velocity and depth, in different conditions of the 
stream, the surface velocity can be obtained by simply observing the 
depth of the stream, and from this the mean velocity and discharge 
can be calculated. Let z be the depth of the stream, and v a the surface 
velocity, both measured at the thread of the stream. Then v<? = cz; 
where c is a constant which for the Solani aqueduct had the values 
1-9 to 2, the depths being 6 to 10 ft., and the velocities 3 J to 4J ft. 
Without any assumption of a formula, however, the surface velocities, 
or still better the mean velocities, for different conditions of the 
stream may be plotted on a diagram in which the abscissae are depths 
and the ordinates velocities. The continuous curve through points so 
found would then always give the velocity for any observed depth of 
the stream, without the need of making any new float or current 
meter observations. 

§ 147. Mean Velocity determined by observing a Series of Surface 
Velocities. — The ratio of the mean velocity to the surface velocity 
in one longitudinal section is better ascertained than the ratio of 
the central surface velocity to the mean velocity of the whole cross 
section. Suppose the river divided into a number of compartments 
by equidistant longitudinal planes, and the surface velocity observed 
in each compartment. From this the mean velocity in each com- 
partment and the discharge can be calculated. The sum of the 
partial discharges will be the total discharge of the stream. When 
wires or ropes can be stretched across the stream, the compartments 
can be marked out by tags attached to them. Suppose two such 
ropes stretched across the stream, and floats dropped in above the 
upper rope. By observing within which compartment the path of 
the float lies, and noting the time of transit between the ropes, the 
surface velocity in each compartment can be ascertained The 
mean velocity in each compartment is 0-85 to o-gi of the surface 
velocity in that compartment. Putting k for this ratio, and 
vi, v-2 . . . for the observed velocities, in compartments of area 
ill, ik ... then the total discharge is 

Q = HQiv 1 +a 2 Vi+ ... ). 

If several floats are allowed to pass over each compartment, the 
mean of all those corresponding'to one compartment is to be taken 
as the surface velocity of that compartment. 

This method is very applicable in the case of large streams or 
rivers too wide to stretch a rope across. The paths of the floats 
are then ascertained in this way. Let fig. 148 represent a portion 
of the river, which should be straight and free from obstructions. 

Suppose a base line AB measured 
parallel to the thread of the stream, 
and let the mean cross section of 
the stream be ascertained either by 
■ ~J£ sounding the terminal cross sections 
AE, BF, or by sounding a series of 
equidistant cross sections. The 
cross sections are taken at right 
angles to the base line. Observers 
are placed at A and B with theo- 
dolites or box sextants. The floats 
are dropped in from a boat above 
AE, and picked up by another boat 
below BF. An observer with a 
chronograph or watch notes the 
time in which each float passes 
from AE to BF. The method of 
proceeding is this. The observer 
-~-F A sets his theodolite in the direc- 
tion AE, and gives a signal to drop 
a float. B keeps his instrument 
on the float as it comes down. At 
the moment the float arrives at 
C in the line AE, the observer at 
A calls out. B clamps his instrument and reads off the angle ABC, 
and the time observer begins to note the time of transit. B now 
points his instrument in the direction BF, and A keeps the float on 
the cross wire of his instrument. At the moment the float arrives 
at D in the line BF, the observer B calls out,- A clamps his instru- 
ment and reads off the angle BAD, and the time observer notes the 
time of transit from C to D. Thus all the data are determined for 
plotting the path CD of the float and determining its velocity. By 
dropping in a series of floats, a number of surface velocities can be 
determined. When all these have been plotted, the river can be 



A-- 



B> 



ft- 



n 



Fig. 148 



divided into convenient compartments. The observations belonging 
to each compartment are then averaged, and the mean velocity and 
discharge calculated. It is obvious that, as the surface velocity is 
greatly altered by wind, experiments of this kind should be made in 
very calm weather. 

The ratio of the surface velocity to the mean velocity in the same 
vertical can be ascertained from the formulae for the vertical velocity 
curve already given (§ 101). Exner, in Erbkam's Zeitschrift for 1875, 
gave the following convenient formula. Let v be the mean and V 
the surface velocity in any given vertical longitudinal section, the 
depth of which is h 

v/V = (1 +0-I478V h)/{i +0-22I6V h). 

If vertical velocity rods are used instead of common floats, the 
mean velocity is directly determined for the vertical section in 
which the rod floats. No formula of reduction is then necessary. 
The observed velocity has simply to be multiplied by the area of 
the compartment to which it belongs. 

§ 148. Mean Velocity of the Stream from a Series of Mid Depth 
Velocities. — In the gaugings of the Mississippi it was found that 
the mid depth velocity differed by only a very small quantity from 
the mean velocity in the vertical section, and it was uninfluenced by 
wind. If therefore a series of mid depth velocities are determined 
by double floats or by a current meter, they may be taken to be the 
mean velocities of the compartments in which they occur, and no 
formula of reduction is necessary. If floats are used, the method 
is precisely the same as that described in the last paragraph for sur- 
face floats. The paths of the double floats are observed and plotted, 
and the mean taken of those corresponding to each of the compart- 
ments into which the river is divided. The discharge is the sum of 
the products of the observed mean mid depth velocities and the 
areas of the compartments. 

§ 149. P. P. Boileau's Process for Gauging Streams. — Let U be the 
mean velocity at a given section of a stream, V the maximum velocity, 
or that of the principal filament, which is generally a little below the 
surface, W and w the greatest and least velocities at the surface. 
The distance of the principal filament from the surface is generally 
less than one-fourth of the depth of the stream; W is a little less 
than V; and U lies between W and w. As the surface velocities 
change continuously from the centre towards the sides there are at 
the surface two filaments having a velocity equal to U. The deter- 
mination of the position of these filaments, which Boileau terms the 
gauging filaments, cannot be effected entirely by theory. But, for 
sections of a stream in which there are no abrupt changes of depth, 
their position can be very approximately assigned. Let A and / be 
the horizontal distances of the surface filament, having the velocity 
W, from the gauging filament, which has the velocity U, and from 
the bank on one side. Then 

A// = c 4 V{(W+2a;)/7(W T TO)!, 
c being a numerical constant. From gaugings by Humphreys and 
Abbot, Bazin and Baumgarten, the values c =0-919, 0-922 and 
0-925 are obtained. Boileau adopts as a mean value 0-922. Hence, 
if W and w are determined by float gauging or otherwise, A can 
be found, and then a single velocity observation at A ft. from the 
filament of maximum velocity gives, without need of any reduction, 
the mean velocity of the stream. More conveniently W, w, and U 
can be measured from a horizontal surface velocity curve, obtained 
from a series of float observations. 

§ 150. Direct Determination of the Mean Velocity by a Current Meter 
or Darcy Gauge. — The only method of determining the mean velocity 
at a cross section of a stream which involves no assumption of the 
ratio of the mean velocity to other quantities is this — a plank 
bridge is fixed across the stream near its surface. From this, velocities 
are observed at a sufficient number of points in the cross section of 
the stream, evenly distributed over its area. The mean of these is 
the true mean velocity of the stream. In Darcy and Bazin's ex- 
periments on small streams, the velocity was thus observed at 36 
points in the cross section. 

When the stream is too large to fix a bridge across it, the observa- 
tions may be taken from a boat, or from a couple of boats with a 
gangway between them, anchored successively at a series of points 
across the width of the stream. The position of the boat for e=vm 
series of observations is fixed by angular observations to a base line 
on shore. 

§ 151. A. R. Harlacher's Graphic Method of determining the Dis- 
charge jrom a Series of Current Meter Observations. — Let ABC (fig. 
149) be the cross section of a river at which a complete series of 




*p5 

Fig. 149. 

current meter observations have been taken. Let I., II., VI ... be 
the verticals at different points of which the velocities were men ^uted. 



HYDRAULIC MACHINES! 



HYDRAULICS 



»5 



Suppose the depths at I., II., III., . . . (fig. 149), set off as vertical 
ordinates in fig. 150, and on these vertical ordinates suppose the 
velocities set off horizontally at their proper depths. Thus, if v is 
the measured velocity at the depth h from the surface in fig. 149, on 
vertical marked III., then at III. in fig. 150 take cd = h and ac=v. 
Then d is a point in the vertical velocity curve for the vertical III., 
and, all the velocities for that ordinate being similarly set off, the 
curve can be drawn. Suppose all the vertical velocity curves I. . . . 
V. (fig. 150), thus drawn. On each of these figures draw verticals 

corresponding to veloci- 



[ 



R 



m 



V 



0> 1TMI 9 f ^ 

y //«• 1/ V which a 



Fig. 150.' 



ties of x, 2x, i,x . . . ft. 
second. Then for 
cd at III. (fig. 
the depth at 
which a velocity of 2x 
ft. per second existed 
on the vertical III. in 
fig. 149 and if cd is set 
off at III. in fig. 149 it 
gives a point in a curve 
passing through points of the section where the velocity was 2x ft. 
per second. Set off on each of the verticals in fig. 149 all the depths 
thus found in the corresponding diagram in fig. 150. Curves drawn 
through the corresponding points on the verticals are curves of 
equal velocity. 

The discharge of the stream per second may be regarded as a solid 
having the cross section of the river (fig. 149) as a base, and cross 



Left bank- 



out in this way. The upper figure shows the section of the river 
and the positions of the verticals at which the soundings and gaugings 
were taken. The lower gives the curves of equal velocity, worked out 
from the current meter observations, by the aid of vertical velocity 
curves. The vertical scale in this figure is ten times as great as in 
the other. The discharge calculated from the contour curves is 
14-1087 cubic metres per second. In the lower figure some other 
interesting curves are drawn. Thus, the uppermost dotted curve is 
the curve through points at which the maximum velocity was found ; 
it shows that the maximum velocity was always a little below the 
surface, and at a greater depth at the centre than at the sides. The 
next curve shows the depth at which the mean velocity for each 
vertical was found. The next is the curve of equal velocity corre- 
sponding to the mean velocity of the stream; that is, it passes 
through points in the cross section where the velocity was identical 
with the mean velocity of the stream. 

Hydraulic Machines 

§ 152. Hydraulic machines may be broadly divided into two 
classes: (1) Motors, in which water descending from a higher 
to a lower level, or from a higher to a lower pressure, gives up 
energy which is available for mechanical operations; (2) Pumps, 
in which the energy of a steam engine or other motor is expended 
in raising water from a lower to a higher level. A few machines 
such as the ram and jet pump combine the functions of motor 



Riqht bank . 




s S <» =• s S Sfc SS S5 ss 

♦•08 4-80 6-66 7-30 9-2* 9-80 H-82 12-30 l*-fl 14-80 J6-92 17-30 SSI 19-80 22-15 22-30 24.-80 

Discharge per Second = Q = 14-1087 cui> - m 
Curves of ean-aX velocity. 



27-30 



29-43 




Fig. 151. 



sections normal to the plane of fig. 149 given by the diagrams in fig. 
150. The curves of equal velocity may therefore be considered as 
contour lines of the solid whose volume is the discharge of the stream 
per second. Let ilo be the area of the cross section of the river, il u 
£1* ■ ■ • the areas contained by the successive curves of equal velocity, 
or, if these cut the surface of the stream, by the curves and that 
surface. Let x be the difference of velocity for which the successive 
curves are drawn, assumed above for simplicity at 1 ft. per second. 
Then the volume of the successive layers of the solid body whose 
volume represents the discharge, limited by successive planes passing 
through the contour curves, will be 

j*(!2o+$2i), ^(fii-Fty, and so on. 
Consequently the discharge is 

Q=*U(Qb+Q»)+Qi=0!+ -•- +Q»-i}. 
The areas I2o, Q t . . . are easily ascertained by means of the polar 
planimeter. A slight difficulty arises in the part of the solid lying 
above the last contour curve. This will have generally a height 
which is not exactly x, and a form more rounded than the other 
layers and less like a conical frustum. The volume of this may be 
estimated separately, and taken to be the area of its base (the area 
tt») multiplied by i to \ its height. 

Fig. 151 shows the results of one of Harlacher's gaugings worked' 



and pump. It may be noted that constructively pumps are 
essentially reversed motors. The reciprocating pump is a re- 
versed pressure engine, and the centrifugal pump a reversed 
turbine. Hydraulic machine tools are in principle motors com- 
bined with tools, and they now form an important special class. 
Water under pressure conveyed in pipes is a convenient and 
economical means of transmitting energy and distributing it to 
many scattered working points. Hence large and important 
hydraulic systems are adopted in which at a central station 
water is pumped at high pressure into distributing mains, 
which convey it to various points where it actuates hydraulic 
motors operating cranes, lifts, dock gates, and in some cases 
riveting and shearing machines. In this case the head driving 
the hydraulic machinery is artificially created, and it is the con- 
venience of distributing power in an easily applied form to distant 
points which makes the system advantageous. As there is 
some unavoidable loss in creating an artificial head this system 
is most suitable for driving machines which work intermittently 



86 



HYDRAULICS 



[IMPACT AND REACTION 



(see Power Transmission). The development of electrical 
methods of transmitting and distributing energy has led to the 
utilization of many natural waterfalls so situated as to be useless 
without such a means of transferring the power to points where 
it can be conveniently applied. In some cases, as at Niagara, the 
hydraulic power can only be economically developed in very 
large units, and it can be most conveniently subdivided and 
distributed by transformation into electrical energy. Partly 
from the development of new industries such as paper-making 
from wood pulp and electro-metallurgical processes, which 
require large amounts of cheap power, partly from the facility 
with which energy can now be transmitted to great distances 
electrically, there has been a great increase in the utilization 
of water-power in countries having natural waterfalls. According 
to the twelfth census of the United States the total amount of 
water-power reported as used in manufacturing establishments 
in that country was 1,130,431 h.p. in 1870; 1,263,343 h.p. 
in 1890; and 1,727,258 h.p. in 1900. The increase was 8-4% 
in the decade 1870-1880, 3-1% in 1880-1890, and no less than 
36-7% in 1890-1900. The increase is the more striking because 
in this census the large amounts of hydraulic power which are 
transmitted electrically are not included. 

XII. IMPACT AND REACTION OF WATER 
§ 153- When a stream of fluid in steady motion impinges on a 
solid surface, it presses on the surface with a force equal and opposite 
to that by which the velocity and direction of motion of the fluid 
are changed. Generally, in problems on the impact of fluids, it is 
necessary to neglect the effect of friction between the fluid and the 
surface on which it moves. 

During Impact the Velocity of the Fluid relatively to the Surface on 
■which it impinges remains unchanged in Magnitude. — Consider a 
mass of fluid flowing in contact with a solid surface also in motion, 
the motion of both fluid and solid being estimated relatively to the 
earth. Then the motion of the fluid may be resolved into two parts, 
one a motion equal to that of the solid, and in the same direction, the 
other a motion relatively to the solid. The motion which the fluid 
has in common with the solid cannot at all be influenced by the con- 
tact. The relative component of the motion of the fluid can only be 
altered in direction, but not in magnitude. The fluid moving in 
contact with the surface can only have a relative motion parallel to 
the surface, while the pressure between the fluid and solid, if friction 
is neglected, is normal to the surface. The pressure therefore can 
only deviate the fluid, without altering the magnitude of the relative 
velocity. The unchanged common component and, combined with 
it, the deviated relative component give the resultant final velocity, 
which may differ greatly in magnitude and direction from the initial 
velocity. 

From the principle of momentum, the impulse of any mass of 
fluid reaching the surface in any given time is equal to the change 
of momentum estimated in the same direction. The pressure between 
the fluid and surface, in any direction, is equal to the change of 
momentum in that direction of so much fluid as reaches the surface 
in one second. If Pa is the pressure in any direction, m the mass 
of fluid impinging per second, v a the change of velocity in the direction 
of Pa due to impact, then 

Pa=mv a - 
If ;'i (fig. 152) is the velocity and direction of motion before impact, 
v* that after impact, then v is the total change of motion due to 
impact. The resultant pressure of the 
fluid on the surface is in the direction of 
», and is equal to v multiplied by the mass 
impinging per second. That is, putting 
' P for the resultant pressure, 
P = mn. 
Let P be resolved into two components, 
N and T, normal and tangential to the 
direction of motion of the solid on which 
the fluid impinges. Then N is a lateral 
force producing a pressure on the supports 
of the solid, T is an effort which does work on the solid. If u is the 
velocity of the solid, Tm is the work done per second by the fluid in 
moving the solid surface. 

Let Q be the volume, and GQ the weight of the fluid impinging 
per second, and let Vi be the initial velocity of the fluid before striking 
the surface. Then GQ>i 2 /2g is the original kinetic energy of Q cub. 
ft. oi fluid, and the efficiency of the stream considered as an arrange- 
ment for moving the solid surface is 

i,=T«/(GQV/2g). 

§ 154. Jet deviated entirely in one Direction. — Geometrical Solution 

(fig- J53)- — Suppose a jet of water impinges on a surface ac with a 

velocity ab, and let it be wholly deviated in planes parallel to the 

figure. Also let ae be the velocity and direction of motion of the 



surface. Join eb; then the water moves with respect to the surface 
in the direction and with the velocity eb. As this relative velocity 
is unaltered by contact with the surface, take cd = eb, tangent to the 
surface at c, then cd is the relative motion of the water with respect to 
the surface at c. Take df equal and parallel to ae. Then/c (obtained 
by compounding the relative motion of water to surface and common 
velocity of water and surface) is the absolute velocity and direction 




Fig. 152. 




Fig. 153. 

of the water leaving the surface. Take ag equal and parallel to fc. 
Then, since ab is the initial and ag the final velocity and direction of 
motion, gb is the total change of motion of the water. The resultant 
pressure on the plane is in the direction gb. Join eg. In the triangle 
gae, ae is equal and parallel to df, and ag to fc. Hence eg is equal and 
parallel to cd. But cd = eb = relative motion of water and surface. 
Hence the change of motion of the water is represented in magnitude 
and direction by the third side of an isosceles triangle, of which the 
other sides are equal to the relative velocity of the water and surface, 
and parallel to the initial and final directions of relative motion. 

Special Cases 

§ 155- (1) -4 Jet impinges on a plane surface at rest, in a direction 
normal to the plane (fig. 154). — Let a jet whose section is w impinge 
with a velocity v on a plane surface at rest, 
in a direction normal to the plane. The 
particles approach the plane, are gradually- 
deviated, and finally flow away parallel to 
the plane, having then no velocity in the 
original direction of the jet. The quantity 
of water impinging per second is uiv. The 
pressure on the plane, which is equal to 
the change of momentum per second, is 
P = (G/g)o»». 

(2) If the plane is moving in the direction 
of the jet with the velocity =<=w, the quantity 
impinging per second is w(i> =*=«). The 
momentum of this quantity before impact 
is (G/g)u(u=t=w)ii. After impact, the water 
still possesses the velocity =*=u in the 
direction of the jet; and the momentum, 
in that direction, of so much water as 
impinges in one second, after impact, is 
=fc(G/g)w(»=Ftt)tt. The pressure on the 
plane, which is the change of momentum 

per second, is the difference of these quantities or P = (G/g)w(t)=F«) 2 . 
This differs from the expression obtained in the previous case, 
in that the relative velocity of the water and plane v=fu is sub- 
stituted iorv. Theexpression maybe written P = 2XGXw(d=f u) 2 l2g, 
where the last two terms are the volume of a prism of water whose 
section is the area of the jet and whose length is the head due 
to the relative velocity. The pressure on the plane is twice the 
weight of that prism of water. The work done when the plane 



=i— J 




Fig. 154. 



OF WATER 



HYDRAULICS 



is moving in the same direction as the jet is Pu = {G/g)u{v-ufu 
foot-pounds per second. There issue from the jet w cub. ft. 
per second, and the energy of this quantity before impact is 
(G/2g)wz> 3 . The efficiency of the jet is therefore 17 = 2 (v — u^n/v 3 . 
The value of u which makesthisa maximum isfound by differentiating 
and equating the differential coefficient to zero : — 
d-qjclu = 2 (v 2 - \vu +3» 2 )/i' 3 = o ; 
.'. u =v or jf. 
The former gives a minimum, the latter a maximum efficiency. 
Putting w = \v in the expression above, 
t) max. = s 3 7 . 
(3) If, instead of one plane moving before the jet, a series of planes 
are introduced at short intervals at the same point, the quantity of 
water impinging on the series will be wv instead of a(v-u), and the 
whole pressure = (G/g)wti(o-tt)- The work done is (G/g)avu (v-u). 
The efficiency 7;=-- (G!g)o>vu(v-u)-i-(Gl2g)uv* = 2u(v-u)/v 2 . This be- 
comes a maximum for d-qjdu = 2{v-2u)=o, or M = J», and the ?) = §. 
This result is often used as an approximate expression for the velocity 
of greatest efficiency when a jet of water strikes the floats of a water 
wheel. The work wasted in this case is half the whole energy of the 
jet when the floats run at the best speed. 

§ T 56- (4) Case of a Jet impinging on a Concave Cup Vane, velocity 
of water », velocity of vane in the same direction u (fig. 155), weight 
impinging per second = Gw(v - u). 

If the cup is hemispherical, the water leaves the cup in a 
direction parallel to the jet. Its relative velocity is v-u when ap- 
proaching the cup, and 
-(»-«) when leaving it. 
Hence its absolute velocity 
when leaving the cup is 
u - (v - u) = 2u-v. The 
change of momentum per 
second = (G/g)w(i>-tt) \v- 

(2U-V)\ = 2(G/g)w(fl-K) 2 . 

Comparing this with case 2, 
it is seen that the pressure 
on a hemispherical cup is 
double that on a flat plane. 
p IG jcc The work done on the 

cup = 2(G/g)u (v-u) 2 u foot- 
pounds per second. The efficiency of the jet is greatest when z> = 3«; 
in that case the efficiency = \§. 

If a series of cup vanes are introduced in front of the jet, so that the 
quantity of water acted upon is us instead of u>(v-u), then the whole 
pressure on the chain of cups is (G/g)wi>Si>-(2tt-2))| = 2(G/g)uv(v-u). 
In this case the efficiency is greatest when t> = 2«, and the maximum 
efficiency is unity, or all the energy of the water is expended on the 
cups. 

§157- (5) Caseof a FlatVane oblique to the Jet (fig.156). — Thiscase 
presents some difficulty. The water spreading on the plane in all 



87 




2u 




Fig. 156. 

directions from the point of impact, different particles leave the plane 
with different absolute velocities. Let AB = v = velocity of water, 
AC = m = velocity of plane. Then, completing the parallelogram, 
AD represents in magnitude and direction the relative velocity of 
water and plane. Draw AE normal to the plane and DE parallel to 
the plane. Then the relative velocity AD may be regarded as con- 
sisting of two components, one AE normal, the other DE parallel to 
the plane. On the assumption that friction is insensible, DE is 
unaffected by impact, but AE is destroyed. Hence AE represents 
the entire change of velocity due to impact and the direction of 
that change. The pressure on the plane is in the direction AE, and 
its amount is = mass of water impinging per second X AE. 

Let DAE=0, and let AD=i>. Then AE=i>, cos0; DE=u, sin 9. 
If Q is the volume of water impinging on the plane per second, 
the change of momentum is (G/g)Qiv cos 0. Let AC = w = velocity 
of the plane, and let AC make the angle CAE = 8 with the normal 
to the plane. The velocity of the plane in the direction AE = 
u cos 8. The work of the jet on the plane = (G/g)G> r cos 6 u cos 8. 
The same problem may be thus treated algebraically (fig. 157). 
Let BAF =a, and CAF =5. The velocity v of the water may be de- 
composed into AF=i> cos a normal to the plane, and FB=i> sin a 
parallel to the plane. Similarly the velocity of the plane =w = AC = 
BD can be decomposed into BG = FE = u cos 5 normal to the plane, 
and DG -u sin 8 parallel to the plane. As friction is neglected, the 
velocity of the water parallel to the plane is unaffected by the im- 
pact, but its component v cos o normal to the plane becomes after 



impact the same as that of the plane, that is, u cos 8. Hence the 
change of velocity during impact =AE=t> cos a-u cos 8. The 
change of momentum per second, and consequently the normal 




i Fig. 157. 
pressure on the plane is N = (G/g) Q (» cos a-«cos 8). The pressure 
in the direction in which the plane is moving is P = N cos 8 = (GMQ 

&7T0? - " COS S) C0S S ' and the work done on the P lane is P« = 
(G/g)0> cos a- M cos 8) u cos 8, which is the same expression as 
before, since AE =v r cos =» cos a-u cos 8. 

In one second the plane moves so that the point A (fig. 1-58) comes 
to C, or from the position 
shown in full lines to the 
position shown in dotted 
lines. If the plane remained 
stationary, a length AB=j; 
of the jet would impinge on 
the plane, but, since the plane 
moves in the same direction 
as the jet, only the length 
HB=AB-AH impinges on 
the plane. 

But AH = AC cos 8/ cos o = 
« cos 8/ cos a, and therefore 
HB=s-m cos 8/ cos a. Let 
w = sectional area of jet; ''[■•'' 

volume impinging on plane P 

per second = Q = w(v-u cos IG- I 5°- 

8/cos a) =«(«; cos a-u cos 8)/ cos a. Inserting this in the formulae 
above, we get 

N = (v cos a-u cos 8) 2 ; (1) 

g cos a ' ' v ' 

xi cos 8/ ... 

(v cos a-u cos 8) 2 ; 

cos a ' ' 

cos 8/ 




p_G 1 

g 
G 



Pm 



w u ^"° " (v cos a-u cos 8) J . 

cos a ' 



(2) 
(3) 



Three cases may be distinguished : — 

(a) The plane is at rest. Then u =0, N = (G/g)wi; 2 cos o ; and the 
work done on the plane and the efficiency of the jet are zero. 

(b) The plane moves parallel to the jet. Then 8 = 0, and P« = 
(G/g) au cos 2 a(v — uY, which is a maximum when u = iv. 

When m = |zj then Pu max. = s % (Glg)uv 3 cos 2 a, and the efficiency 
= ij = J cos 2 a. 

(c) The plane moves perpendicularly to the jet. Then S = c.o°-a; 
cosS=sin a; and P M =^ u «2i n _?( t , cos a -Msina) 2 . This is a maxi- 
mum when u = \v cos a. 

When u = \v cos a, the maximum work and the efficiency are the 
same as in the last case. 

§ 158. Best Form of Vane to receive Water. — When water impinges 
normally or obliquely on a plane, it is scattered in all directions 
a | ter impact, and the work carried away by the water is then gener- 
ally lost, from the impossibility of dealing afterwards with streams of 
water deviated in so many directions. By suitably forming the vane, 




Fig. 159. 
however, the water may be entirely deviated in one direction, anfc 
the loss of energy from agitation of the water is entirely avoided. 

Let AB (fig. 159) be a vane, on which a jet of water impinges at 
the point A and in the direction AC. Take AC =n = velocity of 



88 



HYDRAULICS 



[IMPACT AND REACTION 



water, and let AD represent in magnitude and direction the velocity 
of the vane. Completing the parallelogram, DC or AE represents the 
direction in which the water is moving relatively to the vane. If 
the lip of the vane at A is tangential to AE, the water will not have 
its direction suddenly changed when it impinges on the vane, and 
will therefore have no tendency to spread laterally. On the contrary 
it will be so gradually deviated that it will glide up the vane in the 
direction AB. This is sometimes expressed by saying that the vane 
receives the water without shock. 

§ 159. Floats of Poncelet Water Wheels. — Let AC (fig. 160) repre- 
sent the direction of a thin horizontal stream of water having the 




cityu. — The relative velocity = v—u. The final velocity BF (fig. 162} 
is found by combining the relative velocity BD=i> — u tangential to 
the surface with the velocity BE = u of the surface. The intensity of 
normal pressure, as in the last case, is (G/g)t(v — u) 2 /r. The resultant 



velocity v. Let AB be a curved float moving horizontally with 
velocity u. The relative motion of water and float is then initially 
horizontal, and equal to v — u. 

In order that the float may receive the water without shock, it is 
necessary and sufficient that the lip of the float at A should be 
tangential to the direction AC of relative motion. At the end of 
(v — u)/g seconds the float moving with the velocity u comes to the 
position A1B1, and during this time a particle of water received at 
A and gliding up the float with the relative velocity v — u, attains a 
height DE = (zj — u)-J2g. At E the water comes to relative rest. It 
then descends along the float, and when after 2(y—u)/g seconds the 
float has come to A 2 B 2 the water will again have reached the lip at 
Ao and will quit it tangentially, that is, in the direction CA 2 , with 
a relative velocity — (v — u) = — V (2gDE) acquired under the influ- 
ence of gravity. The absolute velocity of the water leaving the float 
is therefore u— (v — u) =211 — v. If u = \ v, the water will drop off the 
bucket deprived of all energy of motion. The whole of the work 
of the jet must therefore have been expended in driving the float. 
The water will have been received without shock and discharged 
without velocity. This is the principle of the Poncelet wheel, but 
in that case the floats move over an arc of a large circle ; the stream 
of water has considerable thickness (about 8 in.); in order to get 
the water into and out of the wheel, it is then necessary that the lip 
of the float should make a small angle (about 15 ) with the direction 
of its motion. The water quits the wheel with a little of its energy of 
motion remaining. 

§ 160. Pressure on a Curved Surface when the Water is deviated 
wholly in one Direction. — When a jet of water impinges on a curved 
surface in such a direction that it is received without shock, the 
pressure on the surface is due to its gradual deviation from its first 
direction. On any portion of the area the pressure is equal and 
opposite to the force required to cause the deviation of so much 
water as rests on that surface. In common language, it is equal 
to the centrifugal force of that quantity of water. 

Case I. Surface Cylindrical and Stationary. — Let AB (fig. 161) 
be the surface, having its axis at O and its radius ~r. Let the 

water impinge at A tangentially, 
and quit the surface tangentially 
at B. Since the surface is at rest, 
v is both the absolute velocity of 
the water and the velocity relatively 
to the surface, and this remains un- 
changed during contact with the 
surface, because the deviating force 
is at each point perpendicular to 
the direction of motion. The water 
is deviated through an angle 
BCD=AOB=<£. Each particle of 
water of weight p exerts radially 
a centrifugal force pv-/rg. Let the 
thickness of the stream = t ft. Then 
the weight of water resting on 
unit of surface = Gt lb ; and the normal pressure per unit of 
surface = n = Gtv-/gr. The resultant of the radial pressures uni- 
formly distiibuted from A to B will be a force acting in the 
direction OC bisecting AOB, and its magnitude will equal that of a 
force of intensity = n, acting on the projection of AB on a plane 
perpendicular to the direction OC. The length of the chord AB = 
2r sin \if>\ let b = breadth of the surface perpendicular to the plane 
of the figure. The resultant pressure on surface 




= R 



, . 4, _ Gt v 2 
= 2rt> sin — X = 



■2 — to 2 sin — 1 
g 2 



2 g r 

which is independent of the radius of curvature. It may be inferred 
that the resultant pressure is the same for any curved surface of the 
same projected area, which deviates the water through the same 
angle. 

Case 2. Cylindrical Surface moving in the Direction AC with Velo- 




Tig. 162. 

normalpressureR = 2(G/g)6<(f— «) 2 sin j <#>. This resultant pressure 
may be resolved into two components P and L, one parallel and tne 
other perpendicular to the direction of the vane's motion. The 
former is an effort doing work on the vane. The latter is a lateral 
force which does no work. 

P = R sin l<t> = (G/g)bt(v-uy{i -cos <#>) ; 
L = R cos i<t> = (G/g)bt(v — u) 2 sin<j>. 

The work done by the jet on the vane is Pu = (G/g)btu(v — tt) 2 (l- 
cos (j>), which is a maximum when m = Jz>. This result can also be 
obtained by considering that the work done on the plane must be 
equal to the energy lost by the water, when friction is neglected. 

If <£ = i8o°, cos <£= — 1, 1 -cos = 2; then P = 2{G/g)bt(v-u)\ 
the same result as for a concave cup. 

§ 161. Position which a Movable Plane takes in Flowing Water. — ■ 
When a rectangular plane, movable about an axis parallel to one of 
its sides, is placed in an in- 
definite current of fluid, it 
takes a position such that the 
resultant of the normal pres- 
sures on the two sides of the 
axis passes through the axis. 
If, therefore, planes pivoted 
so that the ratio a/b (fig. 163) 
is varied are placed in water, 
and the angle they make with 
the direction of the stream is 
observed, the position of the 
resultar.t of the pressures on Fig. 163. 

the plane is determined for 

different angular positions. Experiments of this kind have been 
made by Hagen. Some of his results are given in the following 
table : — 




1 


Larger plane. 


Smaller Plane. 


a/b = 1 -o 


<t> = .-.. 


4> = 9o° 


0-9 


7 K 


72i° 


o-8 


6o° 


57° 


0-7 


*K 


43° 


o-6 


25° 


29° 


o-5 


13 


13° 


0-4 


8° 


6i° 


o-3 


6i° 




0-2 


4° 






§ 162. Direct Action distinguished from Reaction (Rankine, Steam 
Engine, § 147). 

The pressure which a jet exerts on a vane can be distinguished 
into two parts, viz. : — 

(1) The pressure arising from changing the direct component of 
the velocity of the water into the velocity of the vane. In fig. 
J 53. § : 54i a° cos bae is the direct component of the water's velocity, 
or component in the direction of motion of vane. This is changed 
into the velocity ae of the vane. The pressure due to direct impulse 
is then 

Pi=GQ(ab cos bae — ae)/g. ' • 

For a flat vane moving normally, this direct action is the only action 
producing pressure on the vane. 

(2) The term reaction is applied to the additional action due to 
the direction and velocity with which the water glances off the 
vane. It is this which is diminished by the friction between the 
water and the vane. In Case 2, § 160, the direct pressure is 

Pi = G&*(»-w)7g- 
That due to reaction is 

P 2 = - Gbt{v - m) 2 cos <t>lg. 
If <£<90°, the direct component of the water's motion is not 
wholly converted into the velocity of the vane, and the whoU 



OF WATER] 



HYDRAULICS 



8 9 




Fig. 164. 



pressure due to direct impulse is not obtained. If <£>ao°, cos 1^ is 
negative and an additional pressure due to reaction is obtained 

§ 163. Jet Propeller. — In the case of vessels propelled by a jet of 
water (fig. 164), driven stern wards from orifices at the side of the 
vessel, the water, originally at rest out- 
side the vessel, is drawn into the ship 
and caused to move with the forward 
velocity V of the ship. Afterwards it is 
projected sternwards from the jets with 
a velocity v relatively to the ship, or 
v— V relatively to the earth. If Q is 
the total sectional area of the jets, Shv is 
the quantity of water discharged per 
second. The momentum generated per 
second in a sternward direction is 
(G/g)Sto(t>— V), and this is equal to the forward acting reaction P 
which propels the ship. 

The energy carried away by the water 

= i(Gk)Q-j(v-V)\ 
The useful work done on the ship 

PV = (C/g)Sto(»-V)V. (2) 

Adding (1) and (2), we get the whole work expended on the water, 
neglecting friction: — 

W = i(G/g)Sto(» 2 -V 2 ). 
Hence the efficiency of the jet propeller is 

PVAV = 2V/(»+V). (3) 

This increases towards unity as v approaches V. In other words, 
the less the velocity of the jets exceeds that of the ship, and there- 
fore the greater the area of the orifice of discharge, the greater is the 
efficiency of the propeller. 

In the " Waterwitch " v was about twice V. Hence in this case 
the theoretical efficiency of the propeller, friction neglected, was 
about f. 

§ 164. Pressure of a Steady Stream in a Uniform Pipe on a Plane 
normal to the Direction of Motion. — Let CD (fig. 165) be a plane 



(1) 





\A \Aj \ A a 1 


i i^^f^S^^; '■■ — ""nl 


i ^/r'C' ""- x -"" — '■ I 


. 


: :_ :^IUS5= "^-=1 


_i ~~^>>X'<^^ ; ■ - 1 




i I i ■ 

\A I A! \A B 1 



an expression like that for the pressure of an isolated jet on an 
indefinitely extended plane, with the addition of the term in brackets, 
which depends only on the areas of the stream and the plane. For 
a given plane_ the expression in brackets diminishes as fi increases. 
If il/oi = p, the equation (4) becomes 



R = Go>— ! 

2g I 



■)"!■ 



(40) 



_ . Cc(p-l) 

which is of the form 

R = Gco(i» 2 /2g)K, 
where K depends only on the ratio of the sections of the stream and 
plane. 

For example, let c=o-85, a value which is probable, if we allow 
that the sides of the pipe act as internal borders to an orifice. Then 

p 



Fig. 165. 

placed normally to the stream which, for simplicity, may be sup- 
posed to flow horizontally. The fluid filaments are deviated in 
front of the plane, form a contraction at AiAt, and converge again, 
leaving a mass of eddying water behind the plane. Suppose the 
section A0A0 taken at a point where the parallel motion has not 
begun to be disturbed, and A2A2 where the parallel motion is re- 
established. Then since the same quantity of water with the same 
velocity passes A0A0, A2A2 in any given time, the external forces 
produce no change of momentum on the mass A0A0A2A2, and must 
therefore be in equilibrium. If U is the section of the stream at 
AoAo or AjAj, and u the area of the plate CD, the area of the con- 
tracted section of the stream at A1A1 will be c c (il— w), where c c is the 
coefficient of contraction. Hence, if v is the velocity at AoAo or A2A2, 
and "i>i the velocity at A1A1, 

vU— c c v (CI — «); 

.". fi = vQ/c c (Q — w). ( I ) 

Let pa, pi, p 2 be the pressures at the three sections. Applying 
Bernoulli's theorem to the sections AoAo and A1A1, 

G + 2g G^zg' 
Also, for the sections A1A1 and A 2 A 2 , allowing that the head due 
to the relative velocity Vi—v is lost in shock: — 



P\ . gl 2 _^2 , b 8 , (vi-v) 2 . 
G + 2g G _l "2g" 1 " 2g ' 



(2) 



■ '■po-p2 = G(v 1 -v) 2 /2g; 
or, introducing the value in (1), 

Po -p 2 = ( i( _° -,y»» (3) 

2g\c c (tt-u) ) _ w 

Now the external forces in the direction of motion acting on the 

mass A0A0A2A2 are the pressures pA —pitl at the ends, and the 

reaction — R of the plane on the water, which is equal and opposite 

to the pressure of the water on the plane. As these are in equilibrium, 

(i>o-£ 2 )n-R=0; 

.•■R=G0( ° , -.)¥; ( 4 ) 



K- 



1-176- 



p = 
1 
2 
3 
4 
5 
10 

50 
100 



K = 

CO 

3-66 

1-75 
1-29 

I-IO 

•94 

2-00 

3-50 



The assumption that the coefficient of contraction c c is constant 
for different values of p is probably only true when p is not very 
large. Further, the increase of K for large values of p is contrary to 
experience, and hence it may be inferred that the assumption that ' 
all the filaments have a common velocity Vi at the section A1A1 and 
a common velocity v at the section A2A2 is not true when the stream 
is very much larger than the plane. Hence, in the expression 

R = KGcoz/ 2 /2g, 
K must be determined by experiment in each special case. For a 
cylindrical body putting o> for the section, c c for the coefficient of 
contraction, c c (Q— w) for the area of the stream at A1A1, 

vi=vil/c c (Q— w); D2=!>n/(fi — u) ; 
or, putting p = il/w, 

Vi=vplc c (p — i), v 2 = vpl(p~i). 



R = KiG«D 2 /2g, 



K H(^ra-)H-v-n- 




Then 
where 

Taking c c = o-85 and p=4, Ki =0-467, a value less than before. 
Hence there is less pressure on the cylinder than on the thin plane. 

§ 165. Distribution of Pressure on a Surface on which a Jet impinges 
normally. — The principle of momentum gives readily enough the 
total or resultant pressure of a jet impinging on a plane surface, but 
in some cases it is useful to know the distribution of the pressure. 

The problem in the case in which 
the plane is struck normally, and 
the jet spreads in all directions, is 
one of great complexity, but even 
in that case the maximum intensity 
of the pressure is easily assigned. 
Each layer of water flowing from 
an orifice is gradually deviated 
(fig. 166) by contact with the sur- 
face, and during deviation exercises 
a centrifugal pressure towards the 
axis of the jet. The force exerted 
by each small mass of water is 
normal to its path and inversely as 
the radius of curvature of the path. 
Hence the greatest pressure on the 
plane must be at the axis of the jet, and the pressure must decrease 
from the axis outwards, in some such way as is shown by the curve 
of pressure in fig. 167, the branches of the curve being probably 
asymptotic to the plane. 

For simplicity suppose the jet is a vertical one. Let hi (fig. 167) be 
the depth of the orifice from the free surface, and Vi the velocity of 
discharge. Then, if a; is the area of the orifice, the quantity of water 
impinging on the plane is obviously 

Q = w»i=wV(2gW; 
that is, supposing the orifice rounded, and neglecting the coefficient 
of discharge. 

The velocity with which the fluid reaches the plane is, however, 
greater than this, and may reach the value 

v = V (2gh) ; 
where h is the depth of the plane below the free surface. The 
external layers of fluid subjected throughout, after leaving the 
orifice, to the atmospheric pressure will attain the velocity v, and 
will flow away with this velocity unchanged except by friction. 
The layers towards the interior of the jet, being subjected to a pressure 
greater than atmospheric pressure, will attain a less velocity, and so 
much less as they are nearer the centre of the jet. But the pressure 



Fig. 166. 



9° 



HYDRAULICS 



[IMPACT AND REACTION 



can in no case exceed the pressure i> 5 /2g or h measured in feet of 
water, or the direction of motion of the water would be reversed, and 
there would be reflux. Hence the maximum intensity of the pressure 




Fig. 1 68 shows the pressure curves obtained in three experiments 
with three jets of the sizes shown, and with the free surface level in 
the reservoir at the heights marked. 



Fig. 167. 

of the jet on the plane is h ft. of water. If the pressure curve is 
drawn with pressures represented by feet of water, it will touch the 
free water surface at the centre of the jet. 

Suppose the pressure curve rotated so as to form a solid of revolu- 
tion. The weight of water contained in that solid is the total 
pressure of the jet on the surface, which has already been deter- 
mined. Let V = volume of this solid, then GV is its weight in pounds. 
Consequently 

GV = (G/g)«B l »; 

V = 2«V(«!l)- 

We have already, therefore, two conditions to be satisfied by the 
pressure curve. 

Some very interesting experiments on the distribution of pressure 
on a surface struck by a jet have been made by J. S. Beresford 
(Prof. Papers on Indian Engineering, No. cccxxii.), with a view to 
afford information as to the forces acting on the aprons of weirs. 
Cylindrical jets § in. to 2 in. diameter, issuing from a vessel in 
which the water level was constant, were allowed to fall vertically 
on a brass plate 9 in. in diameter. A small hole in the brass plate 
communicated by a flexible tube with a vertical pressure column. 
Arrangements were made by which this aperture could be moved 
jV in. at a time across the area struck by the jet. The height of the 
pressure column, for each position of the aperture, gave the pressure 
at that point of the area struck by the jet. When the aperture was 



I T , I I 

*---t-Diaii.-99--\ »-p 




Distance from axis of jet in inches. 

Fig. 168. — Curves of Pressure of Jets impinging normally on a Plane. 

exactly in the axis of the jet, the pressure column was very nearly 
level with the free surface in the reservoir supplying the jet; that is, 
the pressure was very nearly v*l2g. As the aperture moved away from 
the axis of the jet, the pressure diminished, and it became insensibly 
small at a distance from the axis of the jet about equal to the dia- 
meter of the jet. Hence, roughly, the pressure due to the jet extends 
over an area about four times the area of section of the jet. 



Experiment i. 


Experiment 2. 


Experiment 3. 




Jet "475 in. diameter. 


Jet '988 in. diameter. 


Jet 19' 5 in. diameter. 




8 <* • 

£JJ 

JSVS 
Bus™ 


< <3 
11 

•;.s 
P 


S 

A 
u 

1° 


Hi 

§0.2 

w (1 ' 

£ =S 


■a 

!-s 

^ a 

c « 
rt"— » 

P 


53 

.at» 

A, 


»- S3 "5 

io.s 


Id 

8-9 

U *j 
C <D 

P 


.5 M 
.S rf 

r 




43 





40-5 


42-I5 





42 


27-15 





26-9 




,, 


•05 


39-40 


i > 


•05 


41-9 


,, 


•08 


26-9 






, 


•1 


37-5-39-5 


,, 


•1 


41-5-41-8 


,, 


•13 


26-8 






, 


■15 


35 


,, 


•15 


4i 


,, 


• 18 


26-5-26-6 






, 


•2 


33-5-37 


,, 


•2 


40-3 


,, 


•23 


26-4-26-5 






, 


•25 


3i 


,, 


■25 


39-2 


,, 


•28 


26-3-26-6 






t 


■3 


21-27 


,, 


•3 


37-5 


27 


•33 


26-2 






, 


•35 


21 


,, 


•35 


34-8 


,, 


•38 


25-9 






, 


•4 


14 


,, 


•45 


27 


j» 


•43 


25-5 






, 


•45 


8 


42-25 


•5 


23 


,, 


•48 


25 






, 


•5 


3-5 


,, 


•55 


i8-5 


,, 


•53 


24-5 






, 


•55 


1 


,, 


•6 


13 


,, 


•58 


24 








•b 


o-5 


,, 


•05 


8-3 


,, 


•63 


23-3 






n 


•t>5 





,, 


•7 


5 


,, 


•68 


22-5 










»» 


•75 


3 


,, 


•73 


21-8 










,, 


•8 


2-2 


M 


•78 


21 










42-15 


•«5 
•95 


1-6 
1 


26-5 

J) 
»» 

H 
>J 


•«3 
•88 

•93 
•98 

1-13 
1-18 
1-23 

1-28 

i-33 
1-38 
1-43 
1-48 

i-53 
1-58 
1-9 


20-3 

19-3 

18 

17 
13-5 
12-5 
io-8 

9-5 
8 

7 

6-3 

5 

4-3 

3-5 

2 





As the general form of the pressure curve has been already indi- 
cated, it may be assumed that its equation is of the form 

y = ab-' 2 - (1) 

But it has already been shown that for jc = o, y = ft, hence a = h. 
To determine the remaining constant, the other condition may be 
used, that the solid formed by rotating the pressure curve represents 
the total pressure on the plane The volume of the solid is 

V = I 2irxydx 

= 2irh I „ 
J 

= (7rA/log 6 6)[-6- l2 ]J 

= Trh/\og e b. 
Using the condition already stated, 

2wV (hhi) =wh/\og e b, 

log e b = (7r/2w) V {hjhi). 

Putting the value of b in (2) in eq. (1), and also r for the radius of 
the jet at the orifice, so that <o=irr 2 , the equation to the pressure 
curve is 



_ 2 
b x xdx 



16 * \kji ■ 



§ 166. Resistance of a Plane moving through a Fluid, or Pressure 
of a Current on a Plane. — When a thin plate moves through the 
air, or through an indefinitely large mass of still water, in a direction 
normal to its surface, there is an excess of pressure on the anterior 
face and a diminution of pressure on the posterior face. Let v he 
the relative velocity of the plate and fluid, the area of the plate, G 
the density of the fluid, h the height due to the velocity, then the 
total resistance is expressed by the equation 

R =/Gfi D 2 /2g pounds =fGtih ; 
where /is a coefficient having about the value 1-3 for a plate moving 
in still fluid, and I -8 for a current impinging on a fixed plane, whether 
the fluid is air or water. The difference in the value of the coefficient 
in the two cases is perhaps due to errors of experiment. There is a 
similar resistance to motion in the case of all bodies of " unfair " 
form, that is, in which the surfaces over which the water slides are 
not of gradual and continuous curvature. 

The stress between the fluid and plate arises chiefly in this way. 



WATER MOTORS] 



HYDRAULICS 



9 1 



The streams of fluid deviated in front of the plate, supposed for 
definiteness to be moving through the fluid, receive from it forward 
momentum. Portions of this forward moving water are thrown off 
laterally at the edges of the plate, and diffused through the surround- 
ing fluid, instead of falling to their original position behind the 
plate. Other portions of comparatively still water are dragged into 
motion to fill the space left behind the plate; and there is thus a 
pressure less than hydrostatic pressure at the back of the plate. The 
whole resistance to the motion of the plate is the sum of the excess of 
pressure in front and deficiency of pressure behind. This resistance 
is independent of any friction or viscosity in the fluid, and is due 
simply to its inertia resisting a sudden change of direction at the 
edge of the plate. 

Experiments made by a whirling machine, in which the plate is 
fixed on a long arm and moved circularly, gave the following values 
of the coefficient /. The method is not free from objection, as the 
centrifugal force causes a flow outwards across the plate. 



Approximate 

Area of Plate 

in sq. ft. 


Values of /. 


Borda. 


Hutton. 


Thibault. 


013 
0-25 
0-63 
1 -l 1 


1-39 
1-49 
1-64 


1-24 
i-43 


1-525 
1-784 





There is a steady increase of resistance with the size of the plate, 
in part or wholly due to centrifugal action. 

P. L. G. Dubuat (1734-1809) made experiments on a plane I ft. 
square, moved in a straight line in water at 3 to 6| ft. per second. 
Calling m the coefficient of excess of pressure in front, and n the 
coefficient of deficiency of pressure behind, so that /=«+», he 
found the following values: — 

ot = i; n =0-433;/= I -433. 
The pressures were measured by pressure columns. Experiments 
by A. J. Morin (1795-1880), G. Piobert (1793-1871) and I. Didion 
(1798-1878) on plates of 0-3 to 2-7 sq. ft. area, drawn vertically 
through water, gave/ = 2-i8; but the experiments were made in a 
reservoir of comparatively small depth. For similar plates moved 
through air they found /= 1-36, a result more in accordance with 
those which precede. 

For a fixed plane in a moving current of water E. Mariotte found 
/=l-25- Dubuat, in experiments in a current of water like those 
mentioned above, obtained the values »» = l-i86; n = 0-670; / = 
1-856. Thibault exposed to wind pressure planes of 1-17 and 2-5 
sq. ft. area, and found/to vary from 1-568 to 2-125, the mean value 
being /= 1-834, a result agreeing well with Dubuat. 

§ 167. Stanton's Experiments on the Pressure of Air on Surfaces. — 
At the National Physical Laboratory, London, T. E. Stanton carried 
out a series of experiments on the distribution of pressure on surfaces 
in a current of air passing through an air trunk. These were on a 
small scale but with exceptionally accurate means of measurement. 
These experiments differ from those already given in that the plane 
is small relatively to the cross section of the current (Proc. Inst. 
Civ. Eng. clvi., 1904). Fig. 169 shows the distribution of pressure 
on a square plate, ab is the plate in 
vertical section, acb the distribution 
of pressure on the windward and adb 
that on the leeward side of the central 
section. Similarly aeb is the distribu- 
tion of pressure on the windward and 
afb on the leeward side of a diagonal 
' section. The intensity of pressure at 
the centre of the plate on the windward 
side was in all cases p = Gv 2 /2g lb per 
sq. ft., where G is the weight of a cubic 
foot of air and v the velocity of the 
current in ft. per sec. On the leeward 
side the negative pressure is uniform 
except near the edges, and its value 
depends on the form of the plate. For 
a circular plate the pressure on the 
leeward side was 0-48 Gv 2 /2g and for 
a rectangular plate 0-66 Gi/ 2 /2g. For 
circular or square plates the resultant 
pressure on the plate was P =0-00126 
11 2 lb per sq. ft. where v is the velocity 
of the current in ft. per sec. On a long 
narrow rectangular plate the resultant pressure was nearly 60% 
greater than on a circular plate. In later tests on larger planes in 
free air, Stanton found resistances 18% greater than those observed 
with small planes in the air trunk. 

§ 168. Case when the Direction of Motion is oblique to the Plane.— 
The determination of the pressure between a fluid and surface in this 
case is of importance in many practical questions, for instance, in 
assigning the load due to wind pressure on sloping and curved roofs, 
and experiments have been made by Hutton, Vince, and Thibault on 
planes moved circularly through air and water on a whirling machine. 



Let AB (fig. 170) be a plane moving in the direction R making 
an angle <j> with the plane. The resultant pressure between the fluid 
and the plane will be a normal 
pressure N. The component R 
of this normal pressure is the 
resistance to the motion of the 
plane and the other component 
L is a lateral force resisted by 
the guides which support the 
plane. Obviously 

R = N sin <f>; 
L = N cos 0. 
In the case of wind pressure on 
a sloping roof surface, R is the 
horizontal and L the vertical 
component of the normal pres- 
sure. 

In experiments with the whirling machine it is the resistance to 
motion, R, which is directly measured. Let P be the pressure on a 
plane moved normally through a fluid. Then, for the same plane 
inclined at an angle tj> to its direction of motion, the resistance was 
found by Hutton to be 

R = P(sin 0)1-842 cos*. 
A simpler and more convenient expression given by Colonel 
Duchemin is 

R = 2P sin 2 0/(i +sin 2 <*>). 
Consequently, the total pressure between the fluid and plane is 

N=2P sin <j>/(l+sin z <f) =2P/(cosec <£ + sin <t>), 
and the lateral force is 

L =2P sin <ji cos 4>/(i +sin 2 <p). 
In 1872 some experiments were made for the Aeronautical Society 
' on the pressure of air on oblique planes. These plates, of I to 2 ft. 
square, were balanced by ingenious mechanism designed by F. H. 
Wenham and Spencer Browning, in such a manner that both the 
pressure in the direction of the air current and the lateral force were 
separately measured. These planes were placed opposite a blast 
from a fan issuing from a wooden pipe 18 in. square. The pressure of 
the blast varied from ^ to 1 in. of water pressure. The following are 
thelresults given in pounds per square foot of the plane, and a com- 
parison of the experimental results with the pressures given by 
Duchemin's rule. These last vajues are obtained by taking P=3-3i, 
the observed pressure on a normal surface : — 



Angle between Plane and Direction ) 
of Blast \ 


15° 


20° 


6o° 


90° 


Horizontal pressure R . . . . 

Lateral pressure L 

Normal pressure VL 2 + R 2 . 
Normal pressure by Duchemin's rule 


0-4 
i-6 
1-65 
1-605 


o-6i 
1-96 
2-05 
2-027 


2-73 
1-26 
3-01 
3-276 


3-3i 

3-3i 
3-31 



Water Motors 

In every system of machinery deriving energy from a natural 
water-fall there exist the following parts: — • 

1. A supply channel or head race, leading the water from the 
highest accessible level to the site of the machine. This may be 
an open channel of earth, masonry or wood, laid at as small a 
slope as is consistent with the delivery of the necessary supply of 
water, or it may be a closed cast or wrought-iron pipe, laid at 
the natural slope of the ground, and about 3 ft. below the surface. 
In some cases part of the head race is an open channel, part 
a closed pipe. The channel often starts from a small storage 
reservoir, constructed near the stream supplying the water motor, 
in which the water accumulates when the motor is not working. 
There are sluices or penstocks by which the supply can be cut 
off when necessary. 

2. Leading from the motor there is a tail race, culvert, or 
discharge pipe delivering the water after it has done its work 
at the lowest convenient level. 

3. A waste channel, weir, or bye- wash is placed at the origin 
of the head race, by which surplus water, in floods, escapes. 

4. The motor itself, of one of the kinds to be described presently, 
which either overcomes a useful resistance directly, as in the case 
of a ram acting on a lift or crane chain, or indirectly by actuating 
transmissive machinery, as when a turbine drives the shafting, 
belting and gearing of a mill. With the motor is usually com- 
bined regulating machinery for adjusting the power and speed 
to the work done. This may be controlled in some cases by 
automatic governing machinery. 



92 



HYDRAULICS 



[WATER MOTORS 



§ 169. Water Motors with Artificial Sources of Energy. — The 
great convenience and simplicity of water motors has led to their 
adoption in certain cases, where no natural source of water 
power is available. In these cases, an artificial source of water 
power is created by using a steam-engine to pump water to a 
reservoir at a great elevation, or to pump water into a closed 
reservoir in which there is great pressure. The water flowing 
from the reservoir through hydraulic engines gives back the 
energy expended, less so much as has been wasted by friction. 
Such arrangements are most useful where a continuously acting 
steam engine stores up energy by pumping the water, while the 
work done by the hydraulic engines is done intermittently. 

§ 170. Energy of a Water-fall. — Let Hi be the total fall of level from 
the point where the water is taken from a natural stream to the 
point where it is discharged into it again. Of this total fall a portion, 
which can be estimated independently, is expended in overcoming 
the resistances of the head and tail races or the supply and discharge 
pipes. Let this portion of head wasted be f) r . Then the available 
head to work the motor is H = H ( — I) r . It is this available head which 
should be used in all calculations of the proportions of the motor. 
Let Q be the supply of water per second. Then GQH foot-pounds 
per second is the gross available work of the fall. The power of the 
fall may be utilized in three ways, (a) The GQ pounds of water may 
be placed on a machine at the highest level, and descending in con- 
tact with it a distance of H ft., the work done will be (neglecting 
losses from friction or leakage) GQH foot-pounds per second, (b) 
Or the water may descend in a closed pipe from the higher to the 
lower level, in which case, with the same reservation as before, the 
pressure at the foot of the pipe will be p = GH pounds per square foot. 
If the water with this pressure acts on a movable piston like that 
of a steam engine, it will drive the piston so that the volume described 
is Q cubic feet per second. Then the work done will be pQ = GHQ 
foot-pounds per second as before, (c) Or lastly, the water may be 
allowed to acquire the velocity v = V 2gH by its descent. The kinetic 
energy of Q cubic feet will then be 2GQi< 2 /g = GQH, and if the water 
is allowed to impinge on surfaces suitably curved which bring it 
finally to rest, it will impart to these the same energy as in the 
previous cases. Motors which receive energy mainly in the three 
ways described in (a), (6), (c) may be termed gravity, pressure and 
inertia motors respectively. Generally, if Q ft. per second of water 
act by weight through a distance hi, at a pressure p due to hi ft. of 
fall, and with a velocity v due to h% ft. of fall, so that /!i+fa-|-/i3 = H, 
then, apart from energy wasted by friction or leakage or imperfection 
of the machine, the work done will be 

GQh i +pQ + (Gk)Q(v'-/2 S )=GQH foot pounds, 
the same as if the water acted simply by its weight while descending 
Hft. 

§ 171. Site for Water Motor. — Wherever a stream flows from 
a higher to a lower level it is possible to erect a water motor. 
The amount of power obtainable depends on the available head 
and the supply of water. In choosing a site the engineer will 
select a portion of the stream where there is an abrupt natural 
fall, or at least a considerable slope of the bed. He will have 
regard to the facility of constructing the channels which are to 
convey the water, and will take advantage of any bend in the river 
which enables him to shorten them. He will have accurate 
measurements made of the quantity of water flowing in the 
stream, and he will endeavour to ascertain the average quantity 
available throughout the year, the minimum quantity in dry 
seasons, and the maximum for which bye-wash channels must 
be provided. In many cases the natural fall can be increased 
by a dam or weir thrown across the stream. The engineer will 
also examine to what extent the head will vary in different 
seasons, and whether it is necessary to sacrifice part of the fall 
and give a steep slope to the tail race to prevent the motor being 
drowned by backwater in floods. Streams fed from lakes which 
form natural reservoirs or fed from glaciers are less variable than 
streams depending directly on rainfall, and are therefore advan- 
tageous for water-power purposes. 

§ 172. Water Power at Holyoke, U.S.A. — About 85 m. from the 
mouth of the Connecticut river there was a fall of about 60 ft. in 
a short distance, forming what were called the Grand Rapids, below 
which the river turned sharply, forming a kind of peninsula on which 
the city of Holyoke is built. In 1845 the magnitude of the water- 
power available attracted attention, and it was decided to build a 
dam across the river. The ordinary flow of the river is 6000 cub. ft. 
per sec, giving a gross power of 30,000 h.p. In dry seasons the 
power is 20,000 h.p., or occasionally less. From above the dam a 
system of canals takes the water to mills on three levels. The first 
canal starts with a width of 140 ft. and depth of 22 ft., and supplies 



the highest range of mills. A second canal takes the water which 
has driven turbines in the highest mills and supplies it to a second 
series of mills. There is a third canal on a still lower level supplying 
the lowest mills. The water then finds its way back to the river. 
With the grant of a mill site is also Lased the right to use the water- 
power. A mill-power is defined as 38 cub. ft. of water per sec. 
during 16 hours per day on a fall of 20 ft. This gives about 60 h.p. 
effective. The charge for the power water is at the rate of 20s. per 
h.p. per annum. 

§ 173. Action of Water in a Water Motor. — Water motors may 
be divided into water-pressure engines, water-wheels and 
turbines. 

Water-pressure engines are machines with a cylinder and piston 
or ram, in principle identical with the corresponding part of a 
steam-engine. The water is alternately admitted to and dis- 
charged from the cylinder, causing a reciprocating action of the 
piston or plunger. It is admitted at a high pressure and dis- 
charged at a low one, and consequently work is done on the piston. 
The water in these machines never acquires a high velocity, and 
for the most part the kinetic energy of the water is wasted. 
The useful work is due to the difference of the pressure of 
admission and discharge, whether that pressure is due to the 
weight of a column of water of more or less considerable height, 
or is artificially produced in ways to be described presently. 

Water-wheels are large vertical wheels driven by water falling 
from a higher to a lower level. In most water-wheels, the water 
acts directly by its weight loading one side of the wheel and so 
causing rotation. But in all water-wheels a portion, and in some 
a considerable portion, of the work due to gravity is first em- 
ployed to generate kinetic energy in the water; during its 
action on the water-wheel the velocity of the water diminishes, 
and the wheel is therefore in part driven by the impulse due to 
the change of .the water's momentum. Water-wheels are there- 
fore motors on which the water acts, partly by weight, partly by 
impulse. 

Turbines are wheels, generally of small size compared with 
water wheels, driven chiefly by the impulse of the water. Before 
entering the moving part of the turbine, the water is allowed 
to acquire a considerable velocity; during its action on the 
turbine this velocity is diminished, and the impulse due to the 
change of momentum drives the turbine. 

In designing or selecting a water motor it is not sufficient to 
consider only its efficiency in normal conditions of working. 
It is generally quite as important to know how it will act with 
a scanty water supply or a diminished head. The greatest 
difference in water motors is in their adaptability to varying 
conditions of working. 

Water-pressure Engines. 

§174. In these the water acts by pressure either due to the 
height of the column in a supply pipe descending from a high- 
level reservoir, or created by pumping. Pressure engines were 
first used in mine-pumping on waterfalls of greater height than 
could at that time be utilized by water wheels. Usually they 
were single acting, the water-pressure lifting the heavy pump 
rods which then made the return or pumping stroke by their 
own weight. To avoid losses by fluid friction and shock the 
velocity of the water in the pipes and passages was restricted 
to from 3 to 10 ft. per second, and the mean speed of plunger to 
1 ft. per second. The stroke was long and the number of strokes 
3 to 6 per minute. The pumping lift being constant, such engines 
worked practically always at full load, and the efficiency was 
high, about 84%. But they were cumbrous machines. They 
are described in Weisbach's Mechanics of Engineering. 

The convenience of distributing energy from a central station 
to scattered working-points by pressure water conveyed in pipes 
— a system invented by Lord Armstrong— has already been 
mentioned. This system has led to the development of a great 
variety of hydraulic pressure engines of very various types. 
The cost of pumping the pressure water to some extent restncts 
its use to intermittent operations, such as working lifts and 
cranes, punching, shearing and riveting machines, forging and 
flanging presses. To keep down the cost of the distributing 



WATER MOTORS] 



HYDRAULICS 



93 



mains very high pressures are adopted, generally 700 lb per 
sq. in. or 1600 ft. of head or more. 

In a large number of hydraulic machines worked by water at 
high pressure, especially lifting machines, the motor consists of a 
direct, single acting ram and cylinder. In a few cases double- 
acting pistons and cylinders are used; but they involve a 
water-tight packing of the piston not easily accessible. In some 
cases pressure engines are used to obtain rotative movement, 
and then two double-acting cylinders or three single-acting 
cylinders are used, driving a crank shaft. Some double-acting 
cylinders have a piston rod half the area of the piston. The 
pressure water acts continuously on the annular area in front 
of the piston. During the forward stroke the pressure on the 
front of the piston balances half the pressure on the back. During 
the return stroke the pressure on the front is unopposed. The 
water in front of the piston is not exhausted, but returns to the 
supply pipe. As the frictional losses in a fluid are independent 
of the pressure, and the work done increases directly as the 
pressure, the percentage loss decreases for given velocities of 
flow as the pressure increases. Hence for high-pressure machines 
somewhat greater velocities are permitted in the passages than 
for low-pressure machines. In supply mains the velocity is 
from 3 to 6 ft. per second, in valve passages 5 to 10 ft. per second, 
or in extreme cases 20 ft. per second, where there is less object 
in economizing energy. As the water is incompressible, slide 
valves must have neither lap nor lead, and piston valves are 
preferable to ordinary slide valves. To prevent injurious com- 
pression from exhaust valves closing too soon in rotative engines i 
with a fixed stroke, small self-acting relief valves are fitted to the 
cylinder ends, opening outwards against the pressure into the 
valve chest. Imprisoned water can then escape without over- 
straining the machines. 

In direct single-acting lift machines, in which the stroke is 
fixed, and in rotative machines at constant speed it is obvious 
that the cylinder must be filled at each stroke irrespective of the 
amount of work to be done. The same amount of water is used 
whether much or little work is done, or whether great or small 
weights are lifted. Hence while pressure engines are very 
efficient at full load, their efficiency decreases as the load de- 
creases. Various arrangements have been adopted to diminish 
this defect in engines working with a variable load. In lifting 
machinery there is sometimes a double ram, a hollow ram 
enclosing a solid ram. By simple arrangements the solid ram 
only is used for small loads, but for large loads the hollow ram is 
locked to the solid ram, and the two act as a ram of larger area. 
In rotative engines the case is more difficult. In Hastie's and 
Rigg's engines the stroke is automatically varied with the load, 
increasing when the load is large and decreasing when it is small. 
But such engines are complicated and have not achieved much 
success. Where pressure engines are used simplicity is generally 
a first consideration, and economy is of less importance. 

§ 175. Efficiency of Pressure Engines. — It is hardly possible to form 
a theoretical expression for the efficiency of pressure engines, but 
some general considerations are useful. Consider the case of a long 
stroke hydraulic ram, which has a fairly constant velocity v during 
the stroke, and valves which are fairly wide open during most of the 
stroke. Let r be the ratio of area of ram to area of valve passage, 
a ratio which may vary in ordinary cases from 4 to 12. Then the 
loss in shock of the water entering the cylinder will be (r — i)V/2g in 
ft. of head. The friction in the supply pipe is also proportional to 
:-. The energy carried away in exhaust will be proportional to v 2 . 
Hence the total hydraulic losses may be taken to be approximately 
!"//2g ft., where f is a coefficient depending on the proportions of the 
machine. Let / be the friction of the ram packing and mechanism 
reckoned in lb per sq. ft. of ram area. Then if the supply-pipe 
pressure driving the machine is p lb per sq. ft., the effective working 
pressure will be 

p — G^v 2 /2g—f lb per sq. ft. 
Let A be the area of the ram in sq. ft., v its velocity in ft. per sac. 
The useful work done will be 

(p — Grv' i /2g—f)Av ft. lb per sec, 
and the efficiency of the machine will be 

T, = {p-GpP[2g-f)Ip : 
This shows that the efficiency increases with the pressure p, and 
diminishes with the speed v, other things being the same. If in 



regulating the engine for varying load the pressure is throttled, 
part of the available head is destroyed at the throttle valve, and 
p in the bracket above is reduced. Direct-acting hydraulic lifts, 
without intermediate gearing, may 
have an efficiency of 95 % during the 
working stroke. If a hydraulic jigger is 
used with ropes and sheaves to change 

the speed of the ram to the speed of Level of Supply 

the lift, the efficiency may be only | ; 

50%. E. B. Ellington has given the 
efficiency of lifts with hydraulic 
balance at 85 % during the working 
stroke. Large pressure engines have 
an efficiency of 85 %, but small rota- 
tive engines probably not more than 
50 % and that only when fully loaded. 



fiarge 



fy 



§ 176. Direct- Acting Hydraulic 
Lift (fig. 171).— This is the 
simplest of all kinds of hydraulic 
motor. A cage W is lifted directly 
by water pressure acting in a 
cylinder C, the length of which is 
a little greater than the lift. A 
ram or plunger R of the same 
length is attached to the cage. 
The water-pressure admitted by a 
cock to the cylinder forces up the 
ram, and when the supply valve is 
closed and the discharge valve 
opened, the ram descends. In 
this case the ram is 9 in. diameter, 
with a stroke of 49 ft. It consists 
of lengths of wrought-iron pipe 
screwed together perfectly water- 
tight, the lower end being closed 
by a cast-iron plug. The ram 
works in a cylinder n in. dia- 
meter of 9 ft. lengths of flanged 
cast-iron pipe. The ram passes 
water-tight through the cylinder 
cover, which is provided with 

double hat leathers to prevent H II1H H 

leakage outwards or inwards. As 
the weight of the ram and cage is 
much more than sufficient to cause 
a descent of the cage, part of the 
weight is balanced. A chain at- 
tached to the cage passes over a 
pulley at the top of 
the lift, and carries 
at its free end a 
balance weight B, Dis^ 
working in T iron 
guides. Water is ad- 
mitted to the cylinder 
from a 4-in. supply 
pipe through a two- 
way slide, worked by 
a rack, spindle and 
endless rope. The 
lift works under 73 
ft. of head, and lifts 
1350 ft) at 2 ft. per 
second. The effi- 
ciency is from 75 to 
80%. 

The principal pre- 
judicial resistance to 
the motion of a ram 

of this kind is the fric- i IBM- -J-wi& '- 't. _ 

tion of the cup leathers, 

which make the joint __ 

between the cylinder p 

and ram. Some ex- ' ' ' 

periments by John Hick give for the friction of these leathers 

the following formula. Let F= the total friction in pounds; 



94 



HYDRAULICS 



[WATER MOTORS 



p = water-pressure in pounds per sq. ft.; 




d = diameter of ram in ft 
k a coefficient. 
Y*=kpd 

£ = 0-00393 if the leathers are new or badly lubricated; 
= 0-00262 if the leathers are in good condition and well lubricated. 

Since the total pressure on the ram is P = \ird?p, the fraction of the 
total pressure expended in overcoming the friction of the leathers is 
F/P = -oo$jd to •0033/d, d being in feet. 

Let H be the height of the pressure column measured from the 
free surface of the supply reservoir to the bottom of the ram in its 
lowest position, H& the height from the discharge reservoir to the 
same point, h the height of the ram above its lowest point at any 
moment, S the length of stroke, J2 the area of the ram, W the weight 
of cage, R the weight of ram, 6 the weight of balance weight, w the 
weight of balance chain per foot run, F the friction of the cup leather 
and slides. Then, neglecting fluid friction, if the ram is rising the 
accelerating force is 

Pi = G(H-fc)Q-R-W+B-w(S-fc)+wA-F, 
and if the ram is descending 

Pj=-G(Hi-A)a+W+R-B+w(S-/t)-wA-F. 
If if = I GJJ, Pi and P 2 are constant throughout the stroke; and 
the moving force in ascending and descending is the same, if 

B=W+R+wS-GQ(H + H 6 )/2. 
Using the values just found for w and B, 

P 1 = P 2 = iGQ(H-Hf,)-F. 
Let W+R+wS + B = U, and let P be the constant accelerating 
force acting on the system, then the acceleration is (P/U)g. The 
velocity at the end of the stroke is (assuming the friction to be 
constant) 

t- = VOPgS/U); 
and the mean velocity of ascent is \v. 

§ 177. Armstrong's Hydraulic Jigger. — This is simply a single- 
acting hydraulic cylinder and ram, provided with sheaves so 
as to give motion to a wire rope or chain. It is used in various 
forms of lift and crane. Fig. 172 shows the arrangement. A 
hydraulic ram or plunger B works in a 
stationary cylinder A. Ram and cylinder 
carry sets of sheaves over which passes a 
chain or rope, fixed at one end to the 
cylinder, and at the other connected over 
guide pulleys to a lift or crane. For each 
pair of pulleys, one on the cylinder and one 
on the ram, the movement of the free end 
of the rope is doubled compared with that 
of the ram. With three pairs of pulleys the 
free end of the rope has a movement equal 
to six times the stroke of the ram, the force 
exerted being in the inverse proportion. 

§ 178. Rotative Hydraulic Engines. — Valve- 
gear mechanism similar in principle to that 
of steam engines can be applied to actuate 
the admission and discharge valves, and the 
pressure engine is then converted into a con- 
tinuously-acting motor. 

Let H be the available fall to work the 
engine after deducting the loss of head in the 
supply and discharge pipes, Q the supply cf 
water in cubic feet per second, and 17 the 
efficiency of the engine. Then the horse-power 
of the engine is 

H.P.=„GQH/5 5 o. 
The efficiency of large slow-moving pressure engines is ij= -66 to -8. 
In small motors of this kind probably ij is not greater than -5. 
Let v be the mean velocity of the piston, then its diameter d is given 
by the relation 

Q = 7rd 2 t'/4 in double-acting engines, 
= ird 2 zi/8 in single-acting engines. 

If there are n cylinders put Q/n for Q in these equations. 

Small rotative pressure engines form extremely convenient 
motors for hoists, capstans or winches, and for driving small 
machinery. The single-acting engine has the advantage that 
the pressure of the piston on the crank pin is always in one 
direction; there is then no knocking as the dead centres are 
passed. Generally three single-acting cylinders are used, so 
that the engine will readily start in all positions, and the driving 
effort on the crank pin is very uniform. 

Brotherhood Hydraulic Engine. — Three cylinders at angles of 120° 
with each other are formed in one casting with the frame. The 




Fig. 173. 



plungers are hollow trunks, and the connecting rods abut in 
cylindrical recesses in them and are connected to a common crank 
pin. A circular valve disk with concentric segmental ports revolves 
at the same rate as the crank over ports in the valve face common to 
the three cylinders. Each cylinder is always in communication with 
either an admission or exhaust port. The blank parts of the circular 
valve close the admission and exhaust ports alternately. The fixed 
valve face is of lignum vitae in a metal recess, and the revolving 
valve of gun-metal. In the case of a small capstan engine the 
cylinders are 35 in. diameter and 3 in. stroke. At 40 revs, per minute, 
the piston speed is 31 ft. 
per minute. The ports 
are 1 in. diameter or-fV 
of the piston area, and 
the mean velocity in 
the ports 6-4 ft. per 
sec. With 700 lb per 
sq. in. water pressure 
and an efficiency of 
50%, the engine is 
about 3 h.p. A com- 
mon arrangement is to 
have three parallel 
cylinders acting on a 
three-throw crank shaft, 
the cylinders oscillating 
on trunnions. 

Hastie' s Engine. — Fig. 
173 shows a similar 
engine made by Messrs 
Hastie of Greenock. G, 
G, G are the three 
plungers which pass out 

of the cylinders through cup leathers, and act on the same crank pin. 
A is the inlet pipe which communicates with the cock B. This cock 
controls the action of the engine, being so constructed that it acts as 
a reversing valve when the handle C is in its extreme positions and 
as a brake_ when in its middle position. With the handle in its 
middle position, the ports of the cylinders are in communication 
with the exhaust. Two passages are formed in the framing leading 
from the cock B to the ends of the cylinders, one being in com- 
munication with the supply pipe A, the other with the discharge 
pipe Q. These passages end as shown at E. The oscillation of the 
cylinders puts them 
alternately in com- 
munication with each of 
these passages, and thus 
the water is alternately 
admitted and exhausted. 
In any ordinary rota- 
tive engine the length of 
stroke is invariable. 
Consequently the con- 
sumption of water de- 
pends simply on the 
speed of the engine, 

irrespective of the effort overcome. If the power of the engine 
must be varied without altering the number of rotations, then 
the stroke must be made variable. Messrs Hastie have con- 
trived an exceedingly ingenious method of varying the stroke 
automatically, in proportion to the amount of work to be done (fig. 
174). The crank pin I 
is carried in a slide H 
moving in a disk M. 
In this is a double 
cam K acting on two 
small steel rollers J, 
L attached to the 
slide H. If the cam 
rotates it moves the 
slide and increases or 
decreases the radius of 
the circle in which the 
crank pin I rotates. 
The disk M is keyed 
on a hollow shaft sur- 
rounding the driving 
shaft P, to which the 
cams are attached. 
The hollow shaft N 
has two snugs to 
which the chains RR 
are attached (fig. 175). 
The shaft P carries the 
spring case SS to which 
also are attached the 

other ends of the chains. When the engine is at rest the springs 
extend themselves, rotating the hollow shaft N and the frame M, 
so as to place the crank pin I at its nearest position to the axis of 
rotation. When a resistance has to be overcome, the shaft N rotates 




Fig. 174. 




Fig. 175. 



WATER MOTORS] 



HYDRAULICS 



95 



relatively to P, compressing the springs, till their resistance balances 
the pressure due to the resistance to the rotation of P. The engine 
then commences to work, the crank pin being in the position in 
which the turning effort just overcomes the resistance. If the 
resistance diminishes, the springs force out the chains and shorten the 
stroke of the plungers, and vice versa. The following experiments, 
on an engine of this kind working a hoist, show how the automatic 
arrangement adjusted the water used to the work done. The lift 
was 22 ft. and the water pressure in the cylinders 80 lb per sq. in. 
Weight lifted, j Chain J ^ ^ 

W ga^nf' in i 7i <° H 16 17 20 „ 



745 
16 



857 969 1081 1 193 



m~® 



§ 179. Accumulator Machinery. — It has already been pointed 
out that it is in some cases convenient to use a steam engine 
to create an artificial head of water, which is afterwards employed 
in driving water-pressure machinery. Where power is required 
intermittently, for short periods, at a number of different points, 
as, for instance, in moving the cranes, lock gates, &c, of a 
dockyard, a separate steam engine and boiler at each point is 
very inconvenient; nor can engines worked from a common 
boiler be used, because of the great loss of heat and the difficulties 
which arise out of condensation in the pipes. If a tank, into 
which water is continuously pumped, can be placed at a great 
elevation, the water can then be used in hydraulic machinery 
in a very convenient way. Each hydraulic machine is put 
in communication with the tank by a pipe, and on opening a 
valve it commences work, using a quantity of water directly 
proportional to the work done. No attendance is required when 
the machine is not working. 

A site for such an elevated tank is, however, seldom available, 
and in place of it a beautiful arrangement termed an accumulator, 
invented by Lord Armstrong, is used. This consists of a tall 
vertical cylinder; into this works a solid ram through cup 
leathers or hemp packing, and the ram is loaded by fixed weights, 
so that the pressure in the cylinder is 700 lb or 800 lb per sq.in. 
In some cases the ram is fixed and the cylinder moves on it. 

The pumping en- 
gines which supply 
the energy that 
is stored in the ac- 
cumulator should 
be a pair coupled 
at right angles, so 
as to start in any 
position. The en- 
gines pump into 
the accumulator 
cylinder till the 
ram is at the top 
of its stroke, when 
by a catch ar- 
rangement acting 
on the engine 
throttle valve 
the engines are 
stopped. If the 
accumulator ram 
descends, in con- 
sequence of water 
being taken to 
work machinery, 
the engines im- 
mediately recom- 
mence working. 
Pipes lead from 
the accumulator 
to each of the 
machines requir- 
ing to be driven, 
and do not require to be of large size, as the pressure is so 
great. 

Fig. 176 shows a diagrammatic way the scheme of a system o' 
accumulator machinery. A is the accumulator, with its ram carry- 



V 



B 




ing a cylindrical wrought-iron tank W, in which weights are placed 
to load the accumulator. At R is one of the pressure engines or 
jiggers, worked from the accumulator, discharging the water after use 
into the tank T. In this case the pressure engine is shown working a 
set of blocks, the fixed block being on the ram cylinder, the running 
block on the ram. The chain running over these blocks works a 
lift cage C, the speed of which is as many times greater than that of 
the ram as there are plies of chain on 
the block tackle. B is the balance 
weight of the cage. 

In the use of accumulators on ship- 
board for working gun gear or steering 
gear, the accumulator ram is loaded by 
springs, or by steam pressure acting on a 
piston much larger than the ram. 

R. H. Tweddell has used accumula- 
tors with a pressure of 2000 lb per 
sq. in. to work hydraulic riveting ma- 
chinery. 

The amount of energy stored in the 
accumulator, having a ram d in. in 
diameter, a stroke of S ft., and deliver- 
ing at p lb pressure per sq. in., is 




—p(PS foot-pounds. 

Thus, if the ram is 9 in., the stroke 20 ft., 
and the pressure 800 lb per sq. in., the 
work stored in the accumulator when the 
ram is at the top of the stroke is 1 ,01 7,600 
foot-pounds, that is, enough to drive a 
machine requiring one horse power for 
about half an hour. As, however, the 
pumping engine replaces water as soon 
as it is drawn off, the working capacity 
of the accumulator is very much greater 
than this. Tweddell found that an ac- 
cumulator charged at 1250 lb discharged 
at 1225 lb per sq. in. Hence the friction 
was equivalent to 12 \ ft) per sq. in. and 
the efficiency 98 %. 

When a very great pressure is required Fig. 177, 

a differential accumulator (fig. 177) is 

convenient. The ram is fixed and passes through both ends of 
the cylinder, but is of different diameters at the_ two ends, 
A and B. Hence if d\, <k are the diameters of the ram in inches and 
p the required pressure in lb per sq. in., the load required is 
ipiridri— dh). An accumulator of this kind used with riveting 
machines has rfi = 5j in., (fe = 4fin. The pressure is 2000 lb per sq. in. 
and the load 5-4 tons. 

Sometimes an accumulator is loaded by water or steam pressure 
instead of by a dead weight. Fig. 178 shows the arrangement. A 
piston A is connected to a plunger B of much 
smaller area. Water pressure, say from town 
mains, is admitted below A, and the high 
pressure water is pumped into and discharged 
from the cylinder C in which B works. If r is 
the ratio of the areas of A and B, then, neglect- 
ing friction, the pressure in the upper cylinder 
is r times that under the piston A. With a 
variable rate of supply and demand from the 
upper cylinder, the piston A rises and falls, 
maintaining always a constant pressure in the 
upper cylinder. 

Water Wheels. 

§ 180. Overshot and High Breast Wheels. 
■ — When a water fall ranges between 10 
and 70 ft. and the water supply is from 3 
to 25 cub. ft. per second, it is possible to 
construct a bucket wheel on which the water 
acts chiefly by its weight. If the variation 
of the head-water level does not exceed 2 ft., 
an overshot wheel may be used (fig. 179). 
The water is then projected over the summit Fig. 178. 

of the wheel, and falls in a parabolic path 
into the buckets. With greater variation of head-water level, a 
pitch-back or high breast wheel is better. The water falls over 
the top of a sliding sluice into the wheel, on the same side as the 
head race channel. By adjusting the height of the sluice, the 
requisite supply is given to the wheel in all positions of the 
head-water level. 

The wheel consists of a cast-iron or wrought-iron axle C 
supporting the weight of the wheel. To this are attached two 




9 6 



HYDRAULICS 



(WATER WHEELS 



sets of arms A of wood or iron, which support circular segmental 
plates, B, termed shrouds. A cylindrical sole plate id extends 
between the shrouds on the inner side. The buckets are formed 




Fig. 179. 

by wood planks or curved wrought-iron plates extending from 
shroud to shroud, the back of the buckets being formed by the 
sole plate. 

The efficiency may be taken at 0-75. Hence, if h.p. is the effective 
horse power, H the available fall, and Q the available water supply 
per second, 

h. p. =o-75(GQH/5 5 o) =0-085 QH. 

If the peripheral velocity of the water wheel is too great, water is 
thrown out of the buckets before reaching the bottom of the fall. 
In practice, the circumferential velocity of water wheels of the kind 
now described is from 4! to 10 ft. per second, about 6 ft. being the 
usual velocity of good iron wheels not of very small size. In order 
that the water may enter the buckets easily, it must have a greater 
velocity than the wheel. Usually the velocity of the water at the 
point where it enters the wheel is from 9 to 12 ft. per second, and 
to produce this it must enter the wheel at a point 16 to 27 in. below 
the head-water level. Hence the diameter of an overshot wheel 
may be 

D = H-iJ toH-2* ft. 
Overshot and high breast wheels work badly in back-water, and hence 
if the tail- water level varies, it is better to reduce the diameter of 
the wheel so that its greatest immersion in flood is not more than 

1 ft. The depth d of the shrouds is about 10 to 16 in. The number 
of buckets may be about 

N=xD/d. 
Let v be the peripheral velocity of the wheel. Then the capacity 
of that portion of the wheel which passes the sluice in one second is 
Qi = i>Z>(D<2-d 2 )/D 

= v b d nearly, 
6 being the breadth of the wheel between the shrouds. If, however, 
this quantity of water were allowed to pass on to the wheel the 
buckets would begin to spill their contents almost at the top of the 
fall. To diminish the loss from spilling, it is not only necessary to 
give the buckets a suitable form, but to restrict the water supply to 
one-fourth or one-third of the gross bucket capacity. Let m be the 
value of this ratio; then, Q being the supply of water per second, 

Q = OT Qi = ntbdv. 
This gives the breadth of the wheel if the water supply is known. 
The form of the buckets should be determined thus. The outer 
element of the bucket should be in the direction of motion of the 
water entering relatively to the wheel, so that the water may enter 
without splashing or shock. The buckets should retain the water as 
long as possible, and the width of opening of the buckets should be 

2 or 3 in. greater than the thickness of the sheet of water entering. 




For a wooden bucket (fig. 180, A), take ab = distance between two 
buckets on periphery of wheel. Make ed = \ eb. and bc = % to \ ab. 
Join cd. For an iron bucket (fig. 180, B), take ed = \ eb; bc= lab. 
Draw cO making an . „ 

angle of lo° to 15° with — -"* -" 

the radius at c. On Oc 
take a centre giving a 
circular arc passing 
near d, and round the 
curve into the radial 
part of the bucket de. 

There are two ways 
in which the power of 
a water wheel is given 
off to the machinery 
driven. In wooden 
wheels and wheels 
with rigid arms, a spur 
or bevil wheel keyed 
on the axle of the 

turbine will transmit FlG - l8 °' 

the power to the shafting. It is obvious that the whole 
turning moment due to the weight of the water is then trans- 
mitted through the arms and axle of the water wheel. When 
the water wheel is an iron one, it usually has light iron 
suspension arms incapable of resisting the bending action due 
to the transmission of the turning effort tc the axle. In that 
case spur segments are bolted to one of the shrouds, and the 
pinion to which the power is transmitted is placed so that the 
teeth in gear are, as nearly as may be, on the line of action of the 
resultant of the weight of the water in the loaded arc of the wheel. 

The largest high breast wheels ever constructed were probably 
the four wheels, each 50 ft. in diameter, and of 125 h.p., erected 
by Sir W. Fairbairn in 1825 at Catrine in Ayrshire. These wheels 
are still working. 

§ 181. Poncelet Water Wheel. — When the fall does not exceed 
6 ft., the best water motor to adopt in many cases is the Poncelet 
undershot water wheel. In this the water acts very nearly in the 
same way as in a turbine, and the Poncelet wheel, although 
slightly less efficient than the best turbines, in normal conditions 
of working, is superior to most of them when working with 
a reduced supply of water. A general notion of the action 
of the water on a Poncelet wheel has already been given in 
§ 159. Fig. 181 shows its construction. The water penned back 
between the side walls of the wheel pit is allowed to flow to the 




Fig. 181. 

wheel under a movable sluice, at a velocity nearly equal to the 
velocity due to the whole fall. The water is guided down a slope 
of 1 in 10, or a curved race, and enters the wheel without shock. 
Gliding up the curved floats it comes to rest, falls back, ami 
acquires at the point of discharge a backward velocity relative 
to the wheel nearly equal to the forward velocity of the wheel. 
Consequently it leaves the wheel deprived of nearly the whole 
of its original kinetic energy. 

Taking the efficiency at o-6o, and putting H for the available fall, 
h.p. for the horse-power, and Q for the water supply per second, 

h.p. = 0-068 QH. 
The diameter D of the wheel may be taken arbitrarily. It should not 
be less than twice the fall and is more often four times the fall. For 
ordinary cases the smallest convenient diameter is 14 ft. with_ a 
straight, or 10 ft. with a curved, approach channel. The radial 



TURBINES] 



HYDRAULICS 



97 



depth of buckei should be at least half the fall, and radius of curvature 
of buckets about half the radius of the wheel. The shrouds are 
usually of cast iron with flanges to receive the buckets. The buckets 
may be of iron | in thick bolted to the flanges with f 6 in. bolts. 

Let H' be the fall measured from the free surface of the head- 
water to the point F where the mean layer enters the wheel ; then the 
velocity at which the water enters is t/ = V (2gH'), and the best 
circumferential velocity of the wheel is V = 0-551) to o-6». The 
number of rotations of the wheel per second is N = V/VD. The 
thickness of the sheet of water entering the wheel is very im- 
portant. The best thickness according to experiment is 8 to 10 
in. The maximum thickness should not exceed 12 to 15 in., when 
there is a surplus water supply. Let e be the thickness of the sheet 
of water entering the wheel, and b its width ; then 

bev = Q ; or b — Q/ev. 
Grashof takes e = £H, and then 

i=6Q/HV(2 g H). 
Allowing for the contraction of the stream, the area of opening 
through the sluice may be 1-25 be to 1-3 be. The inside width of 
the wheel is made about 4 in. greater than b. 

Several constructions have been given for the floats of Poncelet 
wheels. One of the simplest is that shown in figs. 181, 182 

Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, 
OD making angles of 15 with OA. Then BD may be the length of 




WPMBMMPMiZmd^WU/M* 



Fig. 182. 



the close breasting fitted to the wheel. Draw the bottom of the 
head race BC at a slope of 1 in 10. Parallel to this, at distances \e 
and e, draw EF and GH. Then EF is the mean layer and GH the 
surface layer entering the wheel. Join OF, and make OFK = 23°. 
Take FK = o-5 to 0-7 H. Then K is the centre from which the 
bucket curve is struck and KF is the radius. The depth of the 
shrouds must be sufficient to prevent the water from rising over the 
top of the float. It is JH to §H. The number of buckets is not 
very important. They are usually I ft. apart on the circumference 
of the wheel. 

The efficiency of a Poncelet wheel has been found in experiments 
to reach 0-68. It is better to take it at o-6 in estimating the power 
of the wheel, so as to allow some margin. 

In fig. 182 s; is the initial and v the final velocity of the water, 
IV parallel to the vane the relative velocity of the water and wheel, 
and V the velocity of the wheel. 

Turbines. 

§ 182. The name turbine was originally given in France to 
any water motor which revolved in a horizontal plane, the axis 
being vertical. The rapid development of this class of motors 
dates from 1827, when a prize was offered by the Societe 
d'Encouragement for a motor of this kind, which should be 
an improvement on certain wheels then in use. The prize 
was ultimately awarded to Benoit Fourneyron (1802-1867), 
whose turbine, but little modified, is still constructed. 

Classification of Turbines. — In some turbines the whole 
available energy of the water is converted into kinetic energy 
before the water acts on the moving part of the turbine. Such 
turbines are termed Impulse or Action Turbines, and they are 
distinguished by this that the wheel passages are never entirely 
filled by the water. To ensure this condition they must be placed 
a little above the tail water and discharge into free air. Turbines 
in which part only of die available energy is converted into 
kinetic energy before the water enters the wheel are termed 
Pressure or Reaction Turbines. In these there is a pressure 
which in some cases amounts to half the head in the clearance 
space between the guide vanes and wheel vanes. The velocity 
with which the water enters the wheel is due to the difference 
between the pressure due to the head and the pressure in the 
clearance space. In pressure turbines the wheel passages must 



be continuously filled with water for good efficiency, and the 
wheel may be and generally is placed below the tail water level. 

Some turbines are designed to act normally as impulse turbines 
discharging above the tail water level. But the passages are so 
designed that they are just filled by the water. If the tail water 
rises and drowns the turbine they become pressure turbines with 
a small clearance pressure, but the efficiency is not much affected. 
Such turbines are termed Limit turbines. 

Next there is a difference of constructive arrangement of 
turbines, which does not very essentially alter the mode of action 
of the water. In axial flow or so-called parallel flow turbines, 
the water enters and leaves the turbine in a direction parallel 
to the axis of rotation, and the paths of the molecules lie on 
cylindrical surfaces concentric with that axis. In radial outward 
and inward flow turbines, the water enters and leaves the turbine 
in directions normal to the axis of rotation, and the paths of the 
molecules lie exactly or nearly in planes normal to the axis of 
rotation. In outward flow turbines the general direction of flow 
is away from the axis, and in inward flow turbines towards the 
axis. There are also mixed flow turbines in which the water 
enters normally and is discharged parallel to the axis of rotation. 

Another difference of construction is this, that the water may 
be admitted equally to every part of the circumference of the 
turbine wheel or to a portion of the circumference only. In the 
former case, the condition of the wheel passages is always the 
same; they receive water equally in all positions during rotation. 
In the latter case, they receive water during a part of the rotation 
only. The former may be termed turbines with complete 
admission, the latter turbines with partial admission. A reaction 
turbine should always have complete admission. An impulse 
turbine may have complete or partial admission. 

When two turbine wheels similarly constructed are placed on 
the same axis, in order to balance the pressures and diminish 
journal friction, the arrangement may be termed a twin turbine. 

If the water, having acted on one turbine wheel, is then passed 
through a second on the same axis, the arrangement may be 
termed a compound turbine. The object of such an arrangement 
would be to diminish the speed of rotation. 

Many forms of reaction turbine may be placed at any height not 
exceeding 30 ft. above the tail water. They then discharge into 
an air-tight suction pipe. The weight of the column of water 
in this pipe balances part of the atmospheric pressure, and the 
difference of pressure, producing the flow through the turbine, is 
the same as if the turbine were placed at the bottom of the fall. 

I. Impulse Turbines. 
(Wheel passages not filled, and 
discharging above the tail 
water.) 

(a) Complete admission. (Rare.) 

(b) Partial admission. (Usual.) 



II. Reaction Turbines. 

(Wheel passages filled, discharg- 
ing above or below the tail 
water or into a suction-pipe.) 

Always with complete admis- 
sion. 



Axial flow, outward flow, inward flow, or mixed flow. 



Simple turbines ; twin turbines ; compound turbines. 

§ 183. The Simple Reaction Wheel. — It has been shown, in § 162, 
that, when water issues from a vessel, there is a reaction on the 
vessel tending to cause motion in a 
direction opposite to that of the jet. 
This principle was applied in a rotating 
water motor at a very early period, and 
the Scotch turbine, at one time much 
used, differs in no essential respect from 
the older form of reaction wheel. 

The old reaction wheel consisted of a 
vertical pipe balanced on a vertical 
axis, and supplied with water (fig. 183). 
From the bottom of the vertical pipe 
two or more hollow horizontal arms 
extended, at the ends of which were 
orifices from which the water was dis- 
charged. The reaction of the jets caused 
the rotation of the machine. 

Let H be the available fall measured 
from the level of the water in the ver- 
tical pipe to the centres e f the orifices, 
r the radius from the axis of rotation to the centres of the orifices, 
v the velocity of discharge through the jets, a the angular velocity of 







Fig. 183. 



9 8 



HYDRAULICS 



[TURBINES 



the machine. When the machine is at rest the water issues from 
the orifices with the velocity V (2gH) (friction being neglected). But 
when the machine rotates the water in the arms rotates also, and is 
in the condition of a forced vortex, all the particles having the same 
angular velocity. Consequently the pressure in the arms at the 
orifices is H-)-aV 2 /2g ft. of water, and the velocity of discharge 
through the orifices is v = tl (2gH + a 2 r 2 ). If the total area of the 
orifices is «, the quantity discharged from the wheel per second is 

Q=wD=wV(2gH+aV). 
While the water passes through the orifices with the velocity v, the 
orifices are moving in the opposite direction with the velocity ar. 
The absolute velocity of the water is therefore 

v- ar = sl (2gH+aV 2 )-ar. 
The momentum generated per second is (GQ/g)(i>-ar), which is 
numerically equal to the force driving the motor at the radius r. 
The work done by the water in rotating the wheel is therefore 

(GQ/ g)(v-ar)ar foot-pounds per sec. 
The work expended by the water fall is GQH foot-pounds per second. 
Consequently the efficiency of the motor is 

_ (v-ar) ar _ }V2gH+aV 2 -ar)ar 
V ~~ gH ~~ gH 

. ,|H_g 2 H 2 



V2gH-faV 2 



Let 

then T) = i-gR! 2ar+ ... 

which increases towards the limit I as ar increases towards infinity. 
Neglecting friction, therefore, the maximum efficiency is reached 
when the wheel has an infinitely great velocity of rotation. But 
this condition is impracticable to realize, and even, at practicable but 
high velocities of rotation, the friction would considerably reduce the 
efficiency. Experiment seems to show that the best efficiency is reached 
when w = V (2gH). Then the efficiency apart from friction is 
i7 = {V(2o 2 »- 2 )-ar!ar/gH 
=0-4i4aV 2 /gH =0-828, 
about 1 7 % of the energy of the fall being carried away by the water 
discharged. The actual efficiency realized appears to be about 60 %, 
so that about 21 % of the energy of the fall is lost in friction, in 
addition to the energy carried away by the water. 

§ 184. General Statement of Hydrodynamical Principles necessary for 
the Theory of Turbines. 

(a) When water flows through any pipe-shaped passage, such as 
the passage between the vanes of a turbine wheel, the relation be- 
tween the changes of pressure and velocity is given by Bernoulli's 
theorem (§ 29). Suppose that, at a section A of such a passage, hi 
is the pressure measured in feet of water, Vi the velocity, and Z\ the 
elevation above any horizontal datum plane, and that at a section 
B the same quantities are denoted by h%, i> 2 , Zi. Then 

h-hi = (% 2 -fi 2 )/2g +Z2-Z1. (1 ) 

If the flow is horizontal, z 2 =Zi; and 

h-ht - (» 2 2 -V)/2g. (la) 

(b) When there is an abrupt change of section of the passage, or 
an abrupt change of section of the stream due to a contraction, then, 
in applying Bernoulli's equation allowance must be made for the 
loss of head in shock (§ 36). Let »i, Vt be the velocities before and 
after the abrupt change, then a stream of velocity i\ impinges on a 
stream at a velocity v 2 , and the relative velocity is vi-v^. The 
head lost is (t>i-t> 2 ) 2 /2g- Then equation (la) becomes 

hi-h = (i , i 2 -T2 5 )/2g-(i'i-f2) 2 /2g =i> 2 (j>i-%)/g. (2) 

To diminish as much as possible the loss of energy from irregular 
eddying motions, the change of section in the turbine passages must 

be very gradual, and the curva- 
ture without discontinuity. 

(c) Equality of A ngular Impulse 
and Change of Angular Momen- 
tum. — Suppose that a couple, the 
moment of which is M, acts on a 
body of weight W for / seconds, 
during which it moves from Ai 
to A 2 (fig. 184). Let vi be the 
velocity of the body at Ai, ^2 its 
velocity at A 2 , and let p it pi be 
the perpendiculars from C on Vi 
and Vt. Then Mt is termed the 
angular impulse of the couple, and 
the quantity 

is the change of angular momen- 
p g turn relatively to C. Then, from 

"*' the equality of angular impulse 

and change of angular momentum 

m = QNIg)(viprDipi), 
or, if the change of momentum is estimated for one second, 

M=(W/g)(u 2 />2-!>lpl). 




Let n, n be the radii drawn from C to Ai, A 2 , and let w u Wi be the 
components of vi, i> 2 , perpendicular to these radii, making angles 
(3 and a with vi, v%. Then 

Vi = Wi sec ft ; vi = a> 2 sec a ; 
pi = ri cos /3 ; p 2 = r 2 cos a. 
.-. M = (W/g) (u^s-wi) , (3) 

where the moment of the couple is expressed in terms of the radii 
drawn to the positions of the body at the beginning and end of a 
second, and the tangential components of its velocity at those 
points. 

Now the water flowing through a turbine enters at the admission 
surface and leaves at the discharge surface of the wheel, with its 
angular momentum relatively to the axis of the wheel changed. It 
therefore exerts a couple — M tending to rotate the wheel, equal and 
opposite to the couple M which the wheel exerts on the water. Let 
Q cub. ft. enter and leave the wheel per second, and let v>\, Vh be 
the tangential components of the velocity of the water at the receiv- 
ing and discharging surfaces of the wheel, r it r% the radii of those 
surfaces By the principle above, 

- M = (GQ/g) (wr-Wi) . (4) 

If a is the angular velocity of the wheel, the work done by the 
water on the wheel is 

T = Mo= (GQ/g) (it'iri-tt> 2 r 2 ) a foot-pounds per second. (5) 
§ 185. Total and Available Fall. — Let H, be the total difference of 
level from the head-water to the tail-water surface. Of this total 
head a portion is expended in overcoming the resistances of the head 
race, tail race, supply pipe, or other channel conveying the water. 
Let i) p be that loss of head, which varies with the local conditions in 
which the turbine is placed. Then 

H=HH> P 
is the available head for working the turbine, and on this the calcu- 
lations for the turbine should be based. In some cases it is necessary 
to place the turbine above the tail-water level, and there is then a 
fall h from the centre of the outlet surface of the turbine to the tail- 
water level which is wasted, but which is properly one of the losses 
belonging to the turbine itself. In that case the velocities of the 
water in the turbine should be calculated for a head H-b, but the 
efficiency of the turbine for the head H. 

§ 186. Gross Efficiency and Hydraulic Efficiency of a Turbine. — Let 
Td be the useful work done by the turbine, in foot-pounds per 
second, T< the work expended in friction of the turbine shaft, 
gearing, &c, a quantity which varies with the local, conditions in 
which the turbine is placed. Then the effective work done by the 
water in the turbine is 

T = T,+T ( . 
The gross efficiency of the whole arrangement of turbine, races, 
and transmissive machinery is 

7,«=T d /GQH,. (6) 

And the hydraulic efficiency of the turbine alone is 

,=T/GQH. (7) 

It is this last efficiency only with which the theory of turbines is 
concerned. 

From equations (5) and (7) we get 

r/GQH = (GQ/g) (ovi-ws)"! ; 

i) = {wimiliTi) algii. (8) 

This is the fundamental equation in the theory of turbines. In 
general, 1 Wi and w-i, the tangential components of the water's 
motion on entering and leaving the wheel, are completely inde- 
pendent. That the efficiency may be as great as possible, it is 
obviously necessary that kj 2 = o. In that case 

ij = ttVia/gH. (9) 

ari is the circumferential velocity of the wheel at the inlet surface. 
Calling this Vi, the equation becomes 

ij=WiVi/gH. (90) 

This remarkably simple equation is the fundamental equation in 
the theory of turbines. It was first given by Reiche (Turbinen- 
baues, 1877). 

§ 187. General Description of a Reaction Turbine. — Professor 
James Thomson's inward flow or vortex turbine has been 
selected as the type of reaction turbines. It is one of the best 
in normal conditions of working, and the mode of regulation 
introduced is decidedly superior to that in most reaction turbines. 
Figs. 185 and 186 are external views of the turbine case; figs. 
187 and 188 are the corresponding sections; fig. 189 is the 
turbine wheel. The example chosen for illustration has suction 
pipes, which permit the turbine to be placed above the tail- water 
level. The water enters the turbine by cast-iron supply pipes at 
A, and is discharged through two suction pipes S, S. The water 

1 In general, because when the water leaves the turbine wheel it 
ceases to act on the machine. If deflecting vanes or a whirlpool are 
added to a turbine at the discharging side, then Vi may in part depend 
on » 2 , and the statement above is no longer true. 



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99 



on entering the case distributes itself through a rectangular 
supply chamber SC, from which it finds its way equally to the 
four guide-blade passages G, G, G, G. In these passages it 



in equal proportions from each guide-blade passage. It consists 
of a centre plate p (fig. 189) keyed on the shaft aa, which passes 
through stuffing boxes on the suction pipes. On each side of 




Fig. 185. 



Fig. 186. 




Fig. 187 



Fig. 18 



acquires a. velocity about equal to tnat due to half the fall, and is l the centre plate are the curved wheel vanes, on which the pressure 
directed into the wheel at an angle of about io° or 12 with the of the water acts, and the vanes are bounded on each side by 
tangent to its circumference. The wheel W receives the water I dished or conical cover plates c, c. Joint-rings j, j on the cover 



IOO 



HYDRAULICS 



[TURBINES 



plates make a sufficiently water-tight joint with the casing, to 
prevent leakage from the guide-blade chamber into the suction 
pipes. The pressure near the joint rings is not very great, 
probably not one-fourth the total head. The wheel vanes 

receive the water 
without shock, and 
deliver it into central 
spaces, from which it 
flows on either side 
to the suction pipes. 
The mode of regu- 
lating the power of 
the turbine is very 
simple. The guide- 
blades are pivoted to 
the case at their inner 
ends, and they are 
connected by a link- 
work, so that they all 
open and close simul- 
taneously and 
equally. In this way 
the area of opening 
through the guide- 
blades is altered with- 
out materially alter- 
ing the angle or the 
other conditions of 
the delivery into the 
wheel. The guide- 
blade gear may be 
variously arranged. 
In this example four 
spindles, passing through the case, are linked to the guide- 
blades inside the case, and connected together by the links 





Fig. i 




Fig. 190. 

I, I, I on the outside of the case. A worm wheel on one of the 
spindles is rotated by a worm d, the motion being thus slow 



enough to adjust the guide-blades very exactly. These turbines 
are made by Messrs Gilkes & Co. of Kendal 

Fig. 190 shows another arrangement of a similar turbine, with some 
adjuncts not shown in the other drawings. In this case the turbine 
rotates horizontally, and the turbine case is placed entirely below 
the tail water. The water is supplied to the turbine by a vertical 
pipe, over which is a wooden pentrough, containing a strainer, 
which prevents sticks and other solid bodies getting into tH turbine. 
The turbine rests on three foundation stones, and, the pivot for the 
vertical shaft being under water, there is a screw and lever ar-ange- 
ment for adjusting it as it wears. The vertical shaft gives motion 
to the machinery driven by a pair of bevel wheels. On the rigb^ 
are the worm and wheel for working the guide-blade gear. 

§ 188. Hydraulic Power at Niagara. — The largest development of 
hydraulic power is that at Niagara. The Niagara Falls Power 
Company have constructed two power houses on the United States 
side, the first with 10 turbines of 5000 h.p. each, and the second 
with 10 turbines of 5500 h.p. The effective fall is 136 to 140 ft. 
In the first power house the turbines are twin outward flow reaction 
turbines with vertical shafts running at 250 revs, per minute and 
driving the dynamos direct. In the second power house the turbines 




Fig. 191. 

are inward flow turbines with draft tubes or suction pipes. Fig. 191 
shows a section of one of these turbines. There is a balancing 
piston keyed on the shaft, to the under side of which the pressure 
due to the fall is admitted, so that the weight of turbine, vertical 
shaft and part of the dynamo is water borne. About 70,000 h.p. 
is daily distributed electrically from these two power houses. The 
Canadian Niagara Power Company are erecting a power house to 
contain -eleven units of 10,250 h.p. each, the turbines being twin 
inward flow reaction turbines. The Electrical Development Com- 
pany of Ontario are erecting a power house to contain 1 1 units of 
12,500 h.p. each. The Ontario Power Company are carrying out 
another scheme for developing 200,000 h.p. by twin inward flow 
turbines of 12,000 h.p. each. Lastly the Niagara Falls Power and 
Manufacturing Company on the United States side have a station 
giving 35,000 h.p. and are constructing another to furnish 100,000 
h.p. The mean flow of the Niagara river is about 222,000 cub. ft. per 
second with a fall of 160 ft. The works in progress if completed will 
utilize 650,000 h.p. and require 48,000 cub. ft. per second or 2iJ % of 
the mean flow of the river (Unwin, " The Niagara Falls Power 
Stations," Proc. Inst. Mech. Eng., 1906). 

§ 189. Different Forms of Turbine Wheel. — The wheel of a turbine 
or part of the machine on which the water acts is an annular space, 
furnished with curved vanes dividing it into passages exactly or 
roughly rectangular in cross section. For radial flow turbines the 
wheel may have the form A or B, fig. 192, A being most usual with 




«■ To 





Fig. 192. 



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HYDRAULICS 



101 




inward, and B with outward flow turbines. In A the wheel vanes 
are fixed on each side of a centre plate keyed on the turbine shaft. 
The vanes are limited by slightly-coned annular cover plates. In B 
the vanes are fixed on one side of a disk, keyed on the shaft, and 
limited by a cover plate parallel to the disk. Parallel flow or axial 
flow turbines have the wheel as in C. The vanes are limited by two 
concentric cylinders. 

Theory of Reaction Turbines. 

§ 190. Velocity of Whirl and Velocity of Flow. — Let acb (fig. 193) 
be the path of the particles of water in a turbine wheel. That 

path will be in a 
plane normal to the 
axis of rotation in 
radial flow turbines, 
and on a cylindrical 
surface in axial flow 
turbines. At any 
point c of the path 
the water will have 
some velocity v, in 
the direction of a 
tangent to the path. 
That velocity may be 
resolved into two 
components, a whirl- 
FlG. I<«. ' n .£ velocity w in the 

direction of the 
wheel's rotation at the point c, and a component u at right angles 
to this, radial in radial flow, and parallel to the axis in axial flow 
turbines. This second component is termed the velocity of flow. 
Let t» ? , Wo, Uo be the velocity of the water, the whirling velocity and 
velocity of flow at the outlet surface of the wheel, and Vi, Wi, Vi 
the same quantities at the inlet surface of the wheel. Let a and j8 
be the angles which the water's direction of motion makes with the 
direction of motion of the wheel at those surfaces. Then 

Wo = o cos£; u =v An ) / IQ \ 

Wi~ViCosa: tii=v; sin ay 

The velocities of flow are easily ascertained independently from 
the dimensions of the wheel. The velocities of flow at the inlet and 
outlet surfaces of the wheel are normal to those surfaces. Let 
S2„, V.i be the areas of the outlet and inlet surfaces of the wheel, and 
Q the volume of water passing through the wheel per second; then 

Using the notation in fig. 191, we have, for an inward flow turbine 
(neglecting the space occupied by the vanes), 

n =2irr<,(J ; 0,=2irriii. (12a) 

Similarly, for an outward flow turbine, 

i2 = 27rr<,d; Qi=2irnd; (126) 

and, for an axial flow turbine, 

fio=Qi = x(r 2 --ri 2 ). (12c) 

Relative and Common Velocity of the Water and Wheel. — There 
is another way of resolving the velocity of the water. Let V be the 
velocity of the wheel at the point c, fig. 194. Then the velocity of the 

water mayj^e resolved 
into a component V, 
which the water has 
in common with the 
wheel, and a component 
v r , which is the velocity 
of the water relatively 
to the wheel. 

Velocity of Flow. — 

It is obvious that the 

frictional losses of head 

in the wheel passages 

will increase as the 

velocity of flow is 

greater, that is, the 

smaller the wheel is 

made. But if the wheel 

works under water, the 

skin friction of the wheel cover increases as the diameter of the 

wheel is made greater, and in any case the weight of the wheel 

and consequently the journal friction increase as the wheel is made 

larger. It is therefore desirable to choose, for the velocity of flow, 

as large a value as is consistent with the condition that the frictional 

losses in the wheel passages are a small fraction of the total head. 

The values most commonly assumed in practice are these : — 

In axial flow turbines, «„ = «<= Q- I5 to0 " 2 V ( 2 <?H) ; 

In outward flow turbines, ». =o-25V2g(H-f)), 

«» = o-2i to o-l 7V2g( H-f)) ; 
In inward flow turbines, u = Ui =o-izsV (2gH). 
§ 191. Speed of the Wheel. — The best speed of the wheel depends 
partly on the frictional losses, which the ordinary theory of turbines 




Fig. 194. 



disregards. It is best, therefore, to assume for V and Vi values 
which experiment has shown to be most advantageous. 

In axial flow turbines, the circumferential velocities at the mean 
radius of the wheel may be taken 

V„ = Vi=o-6V2gH to o-66V2gH. 
In a radial outward flow turbine, 

V<=o- 5 6V2g(H-b) 
V„ = V<r,,/Ai, 
where r Q , rt are the radii of the outlet and inlet surfaces. 
In a radial inward flow turbine, 

V < =o-66V2ilL 

V = V<r„M. 
If the wheel were stationary and the water flowed through it, the 
water Would follow paths parallel to the wheel vane curves, at least 
when the vanes were so close that irregular motion was prevented. 
Similarly, when the wheel is in motion, the water follows paths rela- 
tively to the wheel, which are curves parallel to the wheel vanes. 
Hence the relative component, v r , of the water's motion at c is tan- 
gential to a wheel vane curve drawn through the point c. Let v», 
V01 "ro be the velocity of the water and its common and relative 
components at the outlet surface of the wheel, and »,-, Vi, vh be the 
same quantities at the inlet surface ; and let 8 and <t> be the angles 
the wheel vanes make with the inlet and outlet surfaces; then 

!>„ 2 = V (v„, ! +V„ s -2V„lVo cos 4>) I , s 

v> =V>ri 2 +Vi 2 -2Vi% cos 61) y ( 3) 

equations which may be used to determine <£ and 8. 

§ 192. Condition determining the Angle of the Vanes at the Outlet 
Surface of the Wheel. — It has been shown that, when the water leaves 
the wheel, it should 
have no tangential 
velocity, if the effici- 
ency is to be as 
great as possible ; 
that is, w<, = 0. Hence, 
from (10), cos /3 = o, 
= 90°, «o = »o, and 
the direction of the 
water's motion is 
normal to the outlet 
surface of the wheel, 
radial in radial flow, 
and axial in axial flow 
turbines. 

Drawing v or u„ 
radial or axial as the 
case may be, and V,, 

tangential to the direction of motion, v r , 
parallelogram of velocities. From fig. 195, 

tan<j>=v fVo = u t ,[V„; (14) 

but <j> is the angle which the wheel vane makes with the outlet 
surface of the wheel, which is thus determined when the velocity 
of flow « and velocity of the wheel V„ are known. When <t> is thus 
determined, 

ti r< , = M<,cosec <#>=V<,V(i+w,,YVo 2 )- (14a) 

Correction of the Angle <j> to allow for Thickness of Vanes. — In 
determining <f>, it is most convenient to calculate its value approxi- 
mately at first, from a value of u obtained by neglecting the thick- 
ness of the vanes. As, however, this angle is the most important 
angle in the turbine, the value should be afterwards corrected to 
allow for the vane thickness. 

Let 

<t>' = tan-Kwo/V,) = tan->(Q/Q„V,) 

be the first or approximate value of <£, and let t be the thickness, 
and n the number of wheel vanes which reach the outlet surface of 
the wheel. As the vanes cut the outlet surface approximately at 
the angle <t>', their width measured on that surface is t cosec $'. 
Hence the space occupied by the vanes on the outlet surface is 

For A, fig. 192, ntd„ cosec 4> 1 

B, fig. 192, ntd cosec <t> >■ (15) 

C, fig. 192, ntir^-n) cosec <t>] 

Call this area occupied by the vanes a. Then the true value of the 
clear discharging outlet of the wheel is U - w, and the true value 
of ito is Qliito - w) . The, corrected value of the angle of the vanes will 
be 

<2> = tan[Q/V<,(n,,-co)]. (16) 

§ 193. Head producing Velocity with which the Water enters the 
Wheel. — Consider the variation of pressure in a wheel passage, 
which satisfies the condition that the sections change so gradually 
that there is no loss of head in shock. When the flow is in a hori- 
zontal plane, there is no work done by gravity on the water passing 
through the wheel. In the case of an axial flow turbine, in which 
the flow is vertical, the fall d between the inlet and outlet surfaces 
should be taken into account. 




Fig. 195. 

can be found by the 



102 



HYDRAULICS 



[TURBINES 



Let Vi, V„ be the velocities of the wheel at the inlet and | 

outlet surfaces, I 

V(, v the velocities of the water, 
m, u„ the velocities of flow, 
Vri,v r „ the relative velocities, 
hi, ho the pressures, measured in feet of water, 
re, r c the radii of the wheel, 

o the angular velocity of the wheel. 
At any point in the path of a portion of water, at radius r, the 
velocity v of the water may be resolved into a component V = ar 
equal to the velocity at that point of the whee', and a relative com- 
ponent v r - Hence the motion of the water may be considered to 
consist of two parts: — (a) a motion identical with that in a forced 
vortex of constant angular velocity a; (i) a flow along curves 
parallel to the wheel vane curves. Taking the latter first, fand using 
Bernoulli's theorem, the change of pressure due to flow through the 
wheel passages is given by the equation 

h'i+VriV^g^h'o+vJ^g; 
h'i —h'o = (iVo 2 — iw 2 )/2g. 

The variation of pressure due to rotation in a forced vortex is 

*"i-&"„ = (V,- s -V<J)/2g. 

Consequently the whole difference of pressure at the inlet and outlet 
surfaces of the wheel is 

hi -ho = k'i+ h'i -h' - h'„ 

= (Vi s -V„ s )/2g + (s„*-lV,- 2 )/2g. (17) 

Case 1. Axial Flow Turbines. — Vi = Vo; and the first term on the 
right, in equation 17, disappears. Adding, however, the work of 
gravity due to a fall of d ft. in passing through the wheel, 

hi-ho^iVrJt-Vri^feg-d. (170) 

Case 2. Outward Flow Turbines. — The inlet radius is less than 
the outlet radius, and (Vi 2 — V„ 2 )/2g is negative. The centrifugal head 
diminishes the pressure at the inlet surface, and increases the velocity 
with which the water enters the wheel. This somewhat increases 
the frictional loss of head. Further, if the wheel varies in velocity 
from variations in the useful work done, the quantity (V* 2 — V„ 2 )/2g 
increases when the turbine speed increases, and vice versa. Conse- 
quently the flow into the turbine increases when the speed increases, 
and diminishes when the speed diminishes, and this again augments 
the variation of speed. The action of the centrifugal head in an out- 
ward flow turbine is therefore prejudicial to steadiness of motion. 
For this reason r„:r,' is made small, generally about 5 : 4. Even 
then a governor is sometimes required to regulate the speed cf the 
turbine. 

Case 3. Inward Flow Turbines. — The inlet radius is greater than 
the outlet radius, and the centrifugal head diminishes the velocity 
of flow into the turbine. This tends to diminish the frictional 
losses, but it has a more important influence in securing steadiness 
of motion. Any increase of speed diminishes the flow into the 
turbine, and vice versa. Hence the variation of speed is less than 
the variation of resistance overcome. In the so-called centre vent 
wheels in America, the ratio ri\r„ is about 5: 4, and then the influ- 
ence of the centrifugal head is not very important. Professor 
James Thomson first pointed out the advantage of a much greater 
difference of radii. By making n:ro = 2:i, the centrifugal head 
balances about half the head in the supply chamber. Then the 
velocity through the guide-blades does not exceed the velocity due 
to half the fall, and the action of the centrifugal head in securing 
steadiness of speed is considerable. 

Since the total head producing flow through the turbine is H — £, 
and of this hi—h is expended in overcoming the pressure in the 
wheel, the velocity of flow into the wheel is 

' f i =C„V!2g(H-l)-(V i 2 -V„ 2 /2g + ( I » ro 2 - P H 2 )/2g)j, (18) 

where c v may be taken 0-96. 
From (14a), 

tV. = V.V(i+«„VV„ 2 ). 
It will be shown immediately that 

iw=M;cosec0; 
or, as this is only a small term, and is on the average 90 , we 
may take, for the present purpose, tw = »> nearly. 

Inserting these values, and remembering that for an axial flow 
turbine V,- = V„, i) = 0, and the fall d in the wheel is to be added, 

For an outward flow turbine, 

,-WW H ^-l(-+«)+S!]' 

For an inward flow turbine, 

§ 194. Angle which the Guide-Blades make with the Circumference 
of the Wheel. — At the moment the water enters the wheel, the 
radial component of the velocity is ut, and the velocity is Vi. Hence, 
if 7 is the angle between the guide-blades and a tangent to the 
wheel 

y=sin~ , (ui/vi). 




This angle can, if necessary, be corrected to allow for the thickness 
of the guide-blades. 

§ 195. Condition determining the Angle of the Vanes at the Inlet 
Surface of the Wheel. — The single condition necessary to be satisfied 
at the inlet surface of 
the wheel is that the 
water should enter the 
wheel without shock. 
This condition is satis- 
fied if the direction of 
relative motion of the 
water and wheel is 
parallel to the first 
element of the wheel 
vanes. 

Let A (fig. 196) be a 
point on the inlet sur- 
face of the wheel, and 
let Vi represent in 
magnitude and direc- 
tion the velocity of the water entering the wheel, and V,- the velocity 
of the wheel. Completing the parallelogram, v r , is the direction of 
relative motion. Hence the angle between vh and Vi is the angle 9 
which the vanes should make with the inlet surface of the wheel. 

§ 196. Example of the Method of designing a Turbine. Professor 
James Thomson's Inward Flow Turbine. — 

Let H =the available fall after deducting loss of head in pipes 
and channels from the gross fall ; 
Q = the supply of water in cubic feet per second; and 
7j =the efficiency of the turbine. 
The work done per second is ijGQH, and the horse-power of the 
turbine is h.p. =i;GQH/550. If t\ is taken at 0-75, an allowance will 
be made for the frictional losses in the turbine, the leakage and the 
friction of the turbine shaft. Then h.p. = o-o85QH. 

The velocity of flow through the turbine (uncorrected for the 
space occupied by the vanes and guide -blad es) may be taken 

Mi=«o=0-I25V2gH, 

in which case about ^th of the energy of the fall is carried away by 
the water discharged. 

The areas of the outlet and inlet surface of the wheel are then 

2*rcdo = 2Widi = Q/o- 1 25V (2gH). 
If we take r„, so that the axial velocity of discharge from the central 
orifices of the wheel is equal to « , we get 

r„ = o-3984V(Q/VH), 

do = To- 

If, to obtain considerable steadying action of the centrifugal head, 

ri =2r , then di =\d . 

Speed of the Wheel. — Let Vi=o-66V2gH, or the speed due to half 
the fall nearly. Then the number of rotations of the turbine per 
second is 

N = V,/27rr ; = 1 -0579V (HV H/Q) ; 
also V„ = Vi>-„/n=o-33V2gH. 

Angle of Vanes with Outlet Surface. 

Tan0 = «„/V„=o-i25/o-33 = -3788; 
= 21° nearly. 
If this value is revised for the vane thickness it will ordinarily 
become about 25 . 

Velocity with which the Water enters the Wheel. — The head pro- 
ducing the velocity is 

H - (Vi 2 /2g) (I + M„ 2 /Vi 2 ) +«i 2 /2g 

= H{i --4356(1 +0-0358) -+-0156} 
= 0-564611. 

Then the velocity is 

Vi = -96V 2g(-5646H) =0-721 V2gH. 
Angle of Guide-Blades. 

Sin 7 = Mi M =0-125/0-721 =0-173; 
y — 10° nearly. 
Tangential Velocity of Water entering Wheel. 
Wi =ViCOS y =0-7101 V 2gH. 
Angle of Vanes at Inlet Surface. 

Cot e = (o»i-Vi)/«i = (-7ioi--66)/-i25 = -40o8; 
9=68° nearly. 
Hydraulic Efficiency of Wheel. 

7/=tt>iVi/gH = -7ioiX-66X2 
= 0-9373- 
This, however, neglects the friction of wheel covers and leakage. 
The efficiency from experiment has been found to be 0-75 to o-8o. 

Impulse and Partial Admission Turbines. 

§ 197. The principal defect of most turbines with complete 

admission is the imperfection of the arrangements for working 

with less than the normal supply. With many forms of reaction 

turbine the efficiency is considerably reduced when the regulating 



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HYDRAULICS 



103 



sluices are partially closed, but it is exactly when the supply 
of water is deficient that it is most important to get out of 
it the greatest possible amount of work. The imperfection of 
the regulating arrangements is therefore, from the practical 
point of view, a serious defect. All turbine makers have sought 
by various methods to improve the regulating mechanism. 
B. Fourneyron, by dividing his wheel by horizontal diaphragms, 
virtually obtained three or more separate radial flow turbines, 
which could be successively set in action at their full power, 
but the arrangement is not altogether successful, because of 
the spreading of the water in the space between the wheel and 
guide-blades. Fontaine similarly employed two concentric 
axial flow turbines formed in the same casing. One was worked 
at full power, the other regulated. By this arrangement the 
loss of efficiency due to the action of the regulating sluice affected 
only half the water power. Many makers have adopted the 
expedient of erecting two or three separate turbines on the same 
waterfall. Then one or more could be put out of action and the 
others worked at full power. All these methods are rather 
palliatives than remedies. The movable guide-blades of 
Professor James Thomson meet the difficulty directly, but they 
are not applicable to every form of turbine. 

C. Callon, in 1840, patented an arrangement of sluices for 
axial or outward flow turbines, which were to be closed success- 
ively as the wat# supply diminished. By preference the sluices 
were closed by pairs, two diametrically opposite sluices forming 
a pair. The water was thus admitted to opposite but equal 
arcs of the wheel, and the forces driving the turbine were sym- 
metrically placed. As soon as this arrangement was adopted, 







Fig. 197. 

a modification of the mode of action of the water in the turbine 
became necessary. If the turbine wheel passages remain full of 
water during the whole rotation, the water contained in each 
passage must be put into motion each time it passes an open 



portion of the sluice, and stopped each time it passes a closed 
portion of the sluice. It is thus put into motion and stopped 
twice in each rotation. This gives rise to violent eddying 
motions and great loss of energy in shock. To prevent this, the 
turbine wheel with partial admission must be placed above the 
tail water, and the wheel passages be allowed to clear themselves 
of water, while passing from one open portion of the sluices to 
the next. 

But if the wheel passages are free of water when they arrive 
at the open guide passages, then there can be no pressure other 
than atmospheric pressure in the clearance space between guides 
and wheel. The water must issue from the sluices with the whole 
velocity due to the head; received on the curved vanes of the 
wheel, the jets must be gradually deviated and discharged with 
a small final velocity only, precisely in the same way as when 
a single jet strikes a curved vane in the free air. Turbines of 
this kind are therefore termed turbines of free deviation. There 
is no variation of pressure in the jet during the Whole time of 
its action on the wheel, and the whole energy of the jet is im- 
parted to the wheel, simply by the impulse due to its gradual 
change of momentum. It is clear that the water may be admitted 
in exactly the same way to any fraction of the circumference 
at pleasure, without altering the efficiency of the wheel. The 
diameter of the wheel may be made as large as convenient, and 
the water admitted to a small fraction of the circumference only. 
Then the number of revolutions is independent of the water 
velocity, and may be kept down to a manageable value. 

§ 198. General Description of an Impulse Turbine or Turbine with 
Free Deviation. — Fig. 197 shows a general sectional elevation of a 
Girard turbine, in 
which the flow is 
axial. The water, . 
admitted above a 
horizontal floor, 
passes down through 
the annular wheel 
containing the guide- 
blades G, G, and 
thence into the re- 
volving wheel WW. 
The revolving wheel 
is fixed to a hollow 
shaft suspended from 
the pivot p. The solid 
internal shaft ss is 
merely a fixed column 
supporting the pivot. 
The advantage of this _ 

is that the pivot is tIG - *9 8 - 

accessible for lubrication and adjustment. B is the mortise bevel 
wheel by which the power of the turbine is given off. The sluices 
are worked by the hand wheel h, which raises them successively, 
in a way to be described presently, d, d are the sluice rods. Figs. 
iq8, 199 show the sectional form of the guide-blade chamber and 
wheel and the curves of the wheel vanes and guide-blades, when 
drawn on a plane de- 
velopment of the cylin- ' 
drical section of the 
wheel; a, a, a are the 
sluices for cutting off 
the water; b, b, b are 
apertures by which the 
entrance or exit of air 
is facilitated as the 
buckets empty and fill. 
Figs. 200, 201 show the 
guide-blade gear, a, a, a 
are the sluice rods as 
before. At the top of 
each sluice rod is a 
small block c, having 
a projecting tongue, 
which slides in the 
groove of the circular 
cam plate d, d. This 
circular plate is sup- 
ported on the frame e, 
and revolves on it by means of the flanged rollers/. Inside, at the 
top, the cam plate is toothed, and gears into a spur pinion connected 
with the hand wheel h. At gg is an inclined groove Or shunt. When 
the tongues of the blocks c, c arrive at g, they slide up to a second 
groove, or the reverse, according as the cam plate is revolved in one 
direction or in the other. As this operation takes place with each 





Fig. 199. 



104 



HYDRAULICS 



[TURBINES 



sluice successively, any number of sluices can be opened or closed as 
desired. The turbine is of 48 horse power on 5' 12 ft. fall, and the 
supply of water varies from 35 to 112 cub. ft. per second. The 




a a a 



Fig. 200. 



efficiency in normal working is given as 73 %. The mean diameter 
of the wheel is 6 ft., and the speed 27-4 revolutions per minute. 

As an example of a partial admission radial flow impulse turbine, 
a 100 h.p. turbine at Immenstadt may be taken. The fall varies 
from 538 to 570 ft. The external diameter of the wheel is 4i ft., and 




*fcA 



QF Q = Q=gD^ gm 



a 



11 



Fig. 201. 




its internal diameter 3 ft. 10 in. Normal speed 400 revs, per minute. 
Water is discharged into the wheel by a single nozzle, shown in fig. 
202 with its regulating apparatus and some of the vanes. The water 

enters the wheel 
at an angle of 22° 
with the direc- 
tion of motion, 
and the final 
angle of the wheel 
vanes is 20 . The 
efficiency on trial 
was from 75 to 
78%. 

§ 199. Theory 
of the Impulse 
Turbine. — The 
theory of the im- 
pulse turbine 
does not essen- 
tially differ from 
that of the re- 
action turbine, 
except that there 
is no pressure in 
the wheel oppos- 
ing the discharge 
from the guide-blades. Hence the velocity with which the water 

enters the wheel is simply 

i\=o-96V2g(H-h), 
where h is the height of the top of the wheel above the tail water. 
If the hydropneumatic system is used, then 6=0. Let Q m be the 
maximum supply of water, n, r 2 the internal and external radii of 
the wheel at the inlet surface; then 

tti=Qm/ta-W -ri*)l. 
The value of m may be about o-45V2g(H-h), whence n, h can be 
determined. 

The guide-blade angle is then given by the equation , 
sin y = M; Ivi =0-45/0-94 = -48; 
7 = 29°. 
The value of «; should, however, be corrected for the space occupied 
by the guide-blades. 

The tangential velocity of the enter ing water is 

# Wi=Vi COS7'=0-82V2g(H-t)). 

The circumferential velocity of t he wheel m ay be (at mean radius) 
V< =o-5V2g(H-h). 



Fig. 202. 



Hence the vane angle at inlet surface is given by the equation 

cote = (a)i-Vi)/«i = (o-82-o-5)/o-45 = -7i; 

= 55°- t 

The relative velocity of the water striking the vane at the inlet 
edge is v,i=m cosec0 = l-22«j. This relative velocity remains 
unchanged during the passage of the water over the vane; conse- 
quently the relative velocity at the point of discharge is v T0 = 1 -222*1. 
Also in an axial flow turbine V = V«. 

If the final velocity of the water is axial, then 

cos = V,,/f r( , = Vi/p,i =0-5/(1 -22 Xo-45)=cos24° 23'. 
This should be corrected for the vane thickness. Neglecting this, 
Wo=iVosin<£=tVisin <£ = «.- cosec sin = o-5«,-. The discharging area 
of the wheel must therefore be greater than the inlet area in the 
ratio of at least 2 to 1. In some actual turbines the ratio is 7 to 3. 
This greater outlet area is obtained by splaying the wheel, as shown 
in the section (fig. 199). 

§ 200. Pelton Wheel. — In the mining district of California about 
i860 simple impulse wheels were used, termed hurdy-gurdy wheels. 
The wheels rotated in a vertical plane, being supported on a hori- 
zontal axis. Round the circumference were fixed flat vanes which 
were struck normally by a jet from a nozzle of size varying with the 
head and quantity of water. Such wheels have in fact long been used. 
They are not efficient, but they are very 
simply constructed. Then attempts were 
made to improve the efficiency, first by using 
hemispherical cup vanes, and then by using 
a double cup vane with a central dividing 
ridge, an arrangement invented by Pelton. 
In this last form the water from the nozzle 
passes half to each side of the wheel, just 
escaping clear of the backs of the advancing 
buckets. Fig. 203 shows a Pelton vane. 
Some small modifications have been made 
by other makers, but they are not of any great importance. 
Fig. 204 shows a complete Pelton wheel with frame and casing, 
supply pipe and nozzle. Pelton wheels have been very largely used 
in America and to some extent in Europe. They are extremely 
simple and easy to construct or repair and on falls of 100 ft. or more 
are very efficient. The jet strikes tangentially to the mean radius 
of the buckets, and the face of the buckets is not quite radial but at 
right angles to the direction of the jet at the point of first impact. 
For greatest efficiency the peripheral velocity of the wheel at the 
mean radius of the buckets should be a little less than half the velocity 
of the jet. As the radius of the wheel can be taken arbitrarily, the 
number of revolutions per minute can be accommodated to that of 
the machinery to be driven. Pelton wheels have been made as small 




Fig. 203. 




I MIL.'l , JJp Ifk \ 1 JJI ■ 




FlG.204. 

as 4 in. diameter, for driving sewing machines, and as large as 24 ft. 
The efficiency on high falls is about 80 %. - When large power is 
required two or three nozzles are used delivering on one wheel. 
The width of the buckets should be not less than seven times the 
diameter of the jet. 

At the Comstock mines, Nevada, there is a 36-in. Pelton wheel 
made of a solid steel disk with phosphor bronze buckets riveted to 
the rim. The head is 2100 ft. and the wheel makes 1 150 revolutions 
per minute, the peripheral velocity being 180 ft. per sec. With a J-in. 
nozzle the wheel uses 32 cub. ft. of water per minute and develops 
100 h.p. At the Chollarshaft, Nevada, there are six Pelton wheels 
on a fall of 1680 ft. driving electrical generators. With f-in. nozzles 
each develops 125 h.p. 

§ 201. Theory of the Pelton Wheel. — Suppose a jet with a velocity 
v strikes tangentially a curved vane AB (fig. 205) moving in the 
same direction with the velocity u. The water will flow over the 
vane with the relative velocity v — u and at B will have the tangential 



TURBINES] 



HYDRAULICS 



105 




Fig. 205. 



relative velocity v — u making .an angle o with the direction of the 
vane's motion. Combining this with the velocity w of the vane, the 
absolute velocity of the water leaving the vane will bew = Be. The com- 
ponent of w in the direction of motion of the vane is Bo = BJ— ab 

= « — (»—«) cos a. Hence 
if Q is the quantity of 
water reaching the vane 
per second the change of 
momentum per second in 
the direction of the vane's 
motion is (GQ/g) [» — {« — 
(v-u)cos o,[] = (GQ/g)(p-«) 
(I + cos a). If a = 0°, 
cos = 1, and the change 
of momentum per second, 
which is equal to the 
effort driving the vane, is 
P =2 (GQ/g) (»-«)! The 
work done on the vane is 
Pu = 2(GQ!g)(v-u)u. If a 
series of vanes are inter- 
posed in succession, the 
quantity of water imping- 
ing on the vanes per second is the total discharge of the nozzle, 
and the energy expended at the nozzle is GQtf 2 /2g. Hence the 
efficiency of the arrangement is, when a = o°, neglecting friction, 

t)=2Pk/GQ!/ 2 =4(ii-w)m/ii 2 , 
which is a maximum and equal to unity if « = §». In that case the 
whole energy of the jet is usefully expended in driving the series of 
vanes. In practice o cannot be quite zero or the water leaving one 
vane would strike the back of the next advancing vane. Fig. 203 
shows a Pelton vane. The water divides each way, and leaves the 
vane on each side in a direction nearly parallel to the direction of 
motion of the vane. The best velocity of the vane is very approxi- 
mately half the velocity of the jet. 

§ 202. Regulation of the Pelton Wheel. — At first Pelton wheels were 
adjusted to varying loads merely by throttling the supply. This 
method involves a total loss of part of the head at the sluice or 
throttle valve. In addition as the working head is reduced, the 
relation between wheel velocity and jet velocity is no longer that of 
greatest efficiency. Next a plan was adopted of deflecting the jet 
so that only part of the water reached the wheel when the load was 
reduced, the rest going to waste. This involved the use of an equal 
quantity of water for large and small loads, but it had, what in some 
cases is an advantage, the effect of preventing any water hammer in 
the supply pipe due to the action of the regulator. In most cases 
now regulation is effected by varying the section of the jet. A 
conical needle in the nozzle can be advanced or withdrawn so as to 
occupy more or less of the aperture of the nozzle. Such a needle can 
be controlled by an ordinary governor. 

§ 203. General Considerations on the Choice of a Type of 
Turbine. — The circumferential speed of any turbine is necessarily 
a fraction of the initial velocity of the water, and therefore M 
greater as the head is greater. In reaction turbines with com- 
plete admission the number of revolutions per minute becomes 
inconveniently great, for the diameter cannot be increased 
beyond certain limits without greatly reducing the efficiency. 
In impulse turbines with partial admission the diameter can be 
chosen arbitrarily and the number of revolutions kept down 
on high falls to any desired amount. Hence broadly reaction 
turbines are better and less costly on low falls, and impulse 
turbines on high falls. For variable water flow impulse turbines 
have some advantage, being more efficiently regulated. On the 
other hand, impulse turbines lose efficiency seriously if their 
speed varies from the normal speed due to the head. If the head 
is very variable, as it often is on low falls, and the turbine must 
run at the same speed whatever the head, the impulse turbine 
is not suitable. Reaction turbines can be constructed so as to 
overcome this difficulty to a great extent. Axial flow turbines 
with vertical shafts have the disadvantage that in addition to 
the weight of the turbine there is an unbalanced water pressure 
to be carried by the footstep or collar bearing. In radial flow 
turbines the hydraulic pressures are balanced. The application of 
turbines to drive dynamos directly has involved some new con- 
ditions. The electrical engineer generally desires a high speed 
of rotation, and a very constant speed at all times. The reaction 
turbine is generally more suitable than the impulse turbine. 
As the diameter of the turbine depends on the quantity of water 
and cannot be much varied without great inefficiency, a difficulty 
arises on low falls. This has been met by constructing four 
independent reaction turbines on the same shaft, each having of 



course the diameter suitable for one-quarter of the whole dis- 
charge, and having a higher speed of rotation than a larger 
turbine. The turbines at Rheinfelden and Chevres are so con- 
structed. To ensure constant speed of rotation when the head 
varies considerably without serious inefficiency, an axial flow 
turbine is generally used. It is constructed of three or four 
concentric rings of vanes, with independent regulating sluices, 
forming practically independent turbines of different radii. 
Any one of these or any combination can be used according to 
the state of the water. With a high fall the turbine of largest 
radius only is used, and the speed of rotation is less than with a 
turbine of smaller radius. On the other hand, as the fall decreases 
the inner turbines are used either singly or together, according 
to the power required. At the Zurich waterworks there are 
turbines of 90 h.p. on a fall varying from 10^ ft. to 4$ ft. The 
power and speed are kept constant. Each turbine has three 
concentric rings. The outermost ring gives 90 h.p. with 105 
cub. ft. per second and the maximum fall. The outer and middle 
compartments give the same power with 140 cub. ft. per second 
and a fall of 7 ft. 10 in. All three compartments working together 
develop the power with about 250 cub. ft. per second. In some 
tests the efficiency was 74% with the outer ring working alone, 
75.4% with the outer and middle ring working and a fall of 
7 ft., and 80-7 % with all the rings working. 

§ 204. Speed Governing.^-'Wheii turbines are used to drive 
dynamos direct, the question of speed regulation is of great im- 
portance. Steam engines using a light elastic fluid can be easily 
regulated by governors acting on throttle or expansion valves. 
It is different, with water turbines using a fluid of great inertia. 




Hand 

Regulator 



Fig. 206. 



In one of the Niagara penstocks there are 400 tons of water 
flowing at 10 ft. per second, opposing enormous resistance to rapid 
change of speed of flow. The sluices of water turbines also are 
necessarily large and heavy. Hence relay governors must be 



IOt) 



HYDRAUlilCS 



[PUMPS 



used, and the tendency of relay governors to hunt must be 
overcome. In the Niagara Falls Power House No. i, each tur- 
bine has a very sensitive centrifugal governor acting on a ratchet 
relay. The governor puts into gear one or other of two ratchets 
driven by the turbine itself. According as one or the other 
ratchet is in gear the sluices are raised or lowered. By a sub- 
sidiary arrangement the ratchets are gradually put out of gear 
unless the governor puts them in gear again, and this prevents the 
over correction of the speed from the lag in the action of the 
governor. In the Niagara Power House No. 2, the relay is an 
hydraulic relay similar in principle, but rather more complicated 
in arrangement, to that shown in figi 206, which is a governor 
used for the 1250 h.p. turbines at Lyons. The sensitive governor 
G opens a valve and puts into action a plunger driven by oil 
pressure from an oil reservoir. As the plunger moves forward 
it gradually closes the oil admission valve by lowering the 
fulcrum end/ of the valve lever which rests on a wedge k> attached 
to the plunger. If the speed is still too high, the governor re- 
opens the valve. In the case of the Niagara turbines the oil 
pressure is 1200 lb per sq. in. One , millimetre of movement of 
the governor sleeve completely opens the relay valve, and the 
relay plunger exerts a force of 50 tons. The sluices can be 
completely opened or shut in twelve seconds. The ordinary 
variation of speed of the turbine with varying load does not 
exceed 1%. If all the load is thrown off, the momentary 
variation of speed is not more than 5 %. To prevent hydraulic 
shock in the supply pipes, a relief valve is provided which opens 
if the pressure is in excess of that due to the head. 

§ 205. The Hydraulic Ram. — The hydraulic ram is an arrange- 
ment by which a quantity of water falling a distance h forces 
a portion of the water to rise to a height k\, greater than h. 
It consists of a supply reservoir (A, fig. 207), into which the water 
enters from some natural stream. A pipe j of considerable 
length conducts the water to a lower level, where it is discharged 
intermittently through a self-acting pulsating valve, at d. The 
supply pipe J may be fitted with a flap valve for stopping the 
ram, and this is attached in some cases to a float, so tlwtt the ram 
starts and stops itself automatically,; according as the supply 
cistern fills or empties. The lower float is just sumcienfc'to keep 
open the flap after it has been raised by the action of the upper 
float. The length of chain is adjusted so that the upper float 
opens the flap when the level in the cistern is at the desired 
height. If the water-level falls below the lower float the flap 
closes. The pipe s should be as long and as straight as possible, 
and as it is subjected to considerable pressure from the sudden 
arrest of the motion of the water, it must be strong and strongly 




Fig. 208. 




Fig. 207. 

jointed, a is an air vessel, and e the delivery pipe leading to 
the reservoir at a higher level than A, into which water is to be 
pumped. Fig. 208 shows in section the construction of the ram 
itself, d is the pulsating discharge valve already mentioned, 
which opens inwards and downwards. The stroke Of the valve 
is regulated by the cotter through the spindle, under which are 
washers by which the amount of fall can be regulated. At 
is a delivery valve, opening outwards, which is often a ball- 
valve but sometimes a flap-valve. The water which is pumped 
passes through this valve into the air vessel a, from which it 
flows by the delivery pipe in a regular stream into the cistern 
to which the water is to be raised. In the vertical chamber 
behind the outer valve a small air vessel is formed, and into 



this opens an aperture -J in. in'diameter, made in a brass screw 
plug b. The hole is reduced ■ to' iV in. in diameter at the outer 
end of the plug and is closed by a small valve opening inwards. 
Through this, during the rebound after each stroke of the ram, 
a small quantity of air is sucked in which keeps the air vessel 
supplied with its elastic cushion of air. 

During the recoil after a sudden closing of the valve d, the 
pressure below it is diminished and the valve opens, permitting 
outflow. In consequence of the flow through this valve, the 
Water in the supply pipe acquires a gradually increasing velocity. 
The upward flow of , 
the water, towards the 
valve d, increases the 
pressure tending to lift 
the valve, and at last, 
if the valve is not too 
heavy, lifts and closes 
it. The forward mo- 
mentum of thecolumn 
in the supply pipe 
being destroyed by the 
stoppage of the flow, 
the water exerts a 
pressure at the end of 
the pipe sufficient to 
open the delivery 
valve o, and to cause 
a portion of the water 
to flow into the air 
vessel. As the water 
in the supply pipe 
comes to rest and 
recoils, the valve d 
opens again and the 
operation is repeated. Part of the energy of the descending 
column is employed in compressing the air at the end of the 
supply pipe arid expanding the pipe itself. This causes a recoil 
of the water which momentarily diminishes the pressure in the 
pipe below the pressure due to the statical head. This assists 
in opening the valve d. The recoil of the water is sufficiently 
great to enable a pump to be attached to the ram body instead 
of the direct rising pipe. With this arrangement a ram working 
with muddy water may be employed to raise clear spring water. 
Instead of lifting the delivery valve as in the ordinary ram, the 
momentum of the column drives a sliding or elastic piston, 
and the recoil brings it back. This piston lifts and forces 
alternately the clear water through ordinary 
pump valves. 

Pumps 
§ 206. The different classes of pumps corre- 
spond almost exactly to the different classes 
of water motors, although the mechanical 
details of the construction are somewhat 
different. They are properly reversed water 
motors. Ordinary reciprocating pumps corre- 
spond to water-pressure engines. Chain 
and bucket pumps are in principle similar 
to water wheels in which the water acts by 
weight. Scoop wheels are similar to undershot water wheels, 
and centrifugal pumps to turbines. 

Reciprocating Pumps are single or double acting, and differ 
from water-pressure engines in that the valves are moved by 
the water instead of by automatic machinery. They may be 
classed thus:-— 

1. Lift Pumps. -—The water drawn through a foot valve on 
the ascent of the pump bucket is forced through the bucket 
valve when it descends, and lifted by the bucket when it reascends. 
Such pumps give an intermittent discharge. 

2. Plunger or Force Pumps, in which the water drawn through 
the foot valve is displaced by the descent of a solid plunger, and 
forced through a delivery valve. They have the advantage that 



ilt ^ini, 




PUMPS] 



HYDRAULICS 



107 



the friction is less than that of lift pumps, and the packing 
round the plunger is easily accessible, whilst that round a lift 
pump bucket is not. The flow is intermittent. 

3. The Double-acting Force Pump is in principle a double 
plunger pump. The discharge fluctuates from zero to a maximum 
and back to zero each stroke, but is not arrested for any 
appreciable time. 

4. Bucket and Plunger Pumps consist of a lift pump bucket 
combined with a plunger of half its area. The flow varies as in 
a double-acting pump. 

5. Diaphragm Pumps have been used, in which the solid 
plunger is replaced by an elastic diaphragm, alternately depressed 
into and raised out of a cylinder. 

As single-acting pumps give an intermittent discharge three 
are generally used on cranks at 120 . But with all pumps the 
variation of velocity of discharge would cause great waste of work 
in the delivery pipes when they are long, and even danger from 
the hydraulic ramming action of the long column of water. 
An air vessel is interposed between the pump and the delivery 
pipes, of a volume from 5 to 100 times the space described by 
the plunger per stroke. The air in this must be replenished 
from time to time, or continuously, by a special air-pump. 
At low speeds not exceeding 30 ft. per minute the delivery of a 
pump is about 90 to 05% of the volume described by the plunger 
or bucket, from 5 to 10% of the discharge being lost by leakage. 
At high speeds the quantity pumped. occasionally exceeds the 
volume described by the plunger, the momentum of the water 
keeping the valves open after the turn of the stroke. 

The velocity of large mining pumps is about 140 ft. per minute, 
the indoor or suction stroke being sometimes made at 250 ft. 
per minute. Rotative pumping engines of large size have a 
plunger speed of 90 ft. per minute. Small rotative pumps are 
run faster, but at some loss of efficiency. Fire-engine pumps 
have a speed of 180 to 220 ft. per minute. 

The efficiency of reciprocating pumps varies very greatly. 
Small reciprocating pumps, with metal valves on lifts of 15 ft., 
were found by Morin to have an efficiency of 16 to 40%, or on 
the average 25%. When used to pump water at considerable 
pressure, through hose pipes, the efficiency rose to from 28 to 
57%, or on the average, with 50 to 100 ft. of lift, about 50%. 
A large pump with barrels 18 in. diameter, at speeds under 60 
ft. per minute, gave the following results: — 

Lift in feet 141 34 47 

Efficiency .... -46 -66 -70 

The very large steam-pumps employed for waterworks, 
with 150 ft. or more of lift, appear to reach an efficiency of 90%, 
not including the friction of the discharge pipes. Reckoned on 
the indicated work of the steam-engine the efficiency may be 
80%. 

Many small pumps are now driven electrically and are usually 
three-throw single-acting pumps driven from the electric motor 
by gearing. It is not convenient to vary the speed of the motor 
to accommodate it to the varying rate of pumping usually required. 
Messrs Hayward Tyler have introduced a mechanism for varying 
the stroke of the pumps (Sinclair's patent) from full stroke 
to nil, without stopping the pumps. 

§ 207. Centrifugal Pump. — For large volumes of water on 
lifts not exceeding about 60 ft. the most convenient pump is 
the centrifugal pump. Recent improvements have made it 
available also for very high lifts. It consists of a wheel or fan 
with curved vanes enclosed in an annular chamber. Water flows 
in at the centre and is discharged at the periphery. The fan 
may rotate in a vertical or horizontal plane and the water may 
enter on one or both sides of the fan. In the latter case there 
is no axial unbalanced pressure. The fan and its casing must 
be filled with water before it can start, so that if not drowned 
there must be a foot valve on the suction pipe. When no special 
attention needs to be paid to efficiency the water may have a 
velocity of 6 to 7 ft. in the suction and delivery pipes. The fan 
often has 6 to 12 vanes. For a double-inlet fan of diameter 
D, the diameter of the inlets is D/2. If Q \i the discharge in 
cub. ft. per second D = about o-6 VQ in average cases. The 



peripheral speed is a little greater than the velocity due to the lift. 
Ordinary centrifugal pumps will have an efficiency of 40 to 60%. 

The first pump of this kind which attracted notice was one 
exhibited by J. G. Appold in 1851, and the special features of 
his pump have been retained in the best pumps since constructed. 
Appold's pump raised continuously a volume of water equal to 
1400 times its own capacity per minute. It had no valves, and 
it permitted the passage of solid bodies, such as walnuts and 
oranges, without obstruction to its working. Its efficiency was 
also found to be good. 

Fig. 209 shows the ordinary form of a centrifugal pump. 
The pump disk and vanes B are cast in one, usually of bronze, 




and the disk is keyed on the driving shaft C. The casing A 
has a spirally enlarging discharge passage into the discharge 
pipe K. A cover L gives access to the pump. S is the suction 
pipe which opens into the pump disk on both sides at D. 

Fig. 210 shows a centrifugal pump differing from ordinary 
centrifugal pumps in one feature only. The water rises through 
a suction pipe S, which divides so as to enter the pump wheel 
W at the centre on each side. The pump disk or wheel is very 
similar to a turbine wheel. It is keyed on a shaft driven by a 
belt on a fast and loose pulley arrangement at P. The water 
rotating in the pump disk presses outwards, and if the speed is 
sufficient a continuous flow is maintained through the pump 
and into the discharge pipe D. The special feature in this pump 
is that the water, discharged by the pump disk with a whirling 
yelocity of not inconsiderable magnitude, is allowed to continue 
rotation in a chamber somewhat larger than the pump. The 
use of this whirlpool chamber was first suggested by Professor 
James Thomson. It utilizes the energy due to the whirling 
velocity of the water which in most pumps is wasted in eddies 
in the discharge pipe. In the pump shown guide-blades are also 
added which have the direction of the stream lines in a free 
vortex. They do not therefore interfere with the action of th"e. 
water when pumping the normal quantity, but only prevent 
irregular motion. At A is a plug by which the pump case is 
filled before starting. If the pump is above the water to be 
pumped, a foot valve is required to permit the pump to be filled. 
Sometimes instead of the foot valve a delivery valve is used, 
an air-pump or steam jet pump being employed to exhaust the 
air from the pump case. 

§ 208. Design and Proportions 0} a Centrifugal Pump.— The design 
of the pump disk is very simple. Let r { , n be the radii of the inlet 
and outlet surfaces of the pump disk, &i, d the clear axial width at 
those radii. The velocity of flow through the pump may be taken 



io8 



HYDRAULICS 



[PUMPS 




Fig. 2io. 




the same as for a turbine. If Q is the quantity pumped, and H the 
lift, 

Mi=0-25V2fiH. (i) 

2-irndi =Q/m>. 
Also in practice 

di-V2Ti .... I 
Hence, f (2) 

r< = -257W(Q/VH).J 
Usually r = 2r>, 

and d =di or jd,- 

according as the disk is parallel-sided or coned. The water enters 
the wheel radially with the velocity «.-, and 

u =Ql2irr„d„. (3) 

Fig. 211 shows the notation adopted for the velocities. 
Suppose the water enters the wheel with the velocity Vi, while 

the velocity of the 
"• » ? wheel is V.-. Com- 

pleting the parallelo- 
gram, vh is the rela- 
tive velocity of the 
water and wheel, and 
is the proper direction 
of the wheel vanes. 
Also, by resolving, tu 
and Wi are the com- 
ponent velocities of 
flow and velocities of 
whir of the velocity k 
&f the water. At the 
outlet surface, v is the 
Fig. 211. finaV velocity of dis- 

charge, and the rest of 
the notation is similar to that for the inlet surface. _ 

Usually the water flows equally in all directions in the eye of the 
wheel, in that case d< is radial. Then, in normal conditions of work- 
ing, at the inlet surface, 

Vi = M; "| 

Wi=0 I /.s 

tane=UilWi J w 

v,i = Ui cosec = V(tti 2 +Vv 2 J u 
If the pump is raising less or more than its proper quantity, fl will 
not satisfy the last condition, and there is then some loss of head in 
shock. 

At the outer circumference of the wheel or outlet surface, 
»ro =«• cosec <t> T 

W —Vo — Mo COt <t> '{■ (5) 

»o = VK 2 + (V,,-M COt<*.) 2 !j 

Variation of Pressure in the Pump I>«fe.— Precisely as in the case 
of turbines, it can be shown that the variation of pressure between 
the inlet and outlet surfaces of the pump is 

h -hi = (Vo 2 -Vi 2 )/2g- (tv<, 2 -iVi 2 )/2«. 

Inserting the values of v r „ iw in (4) and (5), we get for normal 
conditions of working 




ho-h = (V„ ! -Vv 2 )/2g-«„ 2 COseC 2 4./2g + (Mi 2 +Vi 2 )/2g 

= V„ 2 /2g-M 2 cosec 2 0/2g + Z(i 2 /2g. (6) 

Hydraulic Efficiency of the Pump. — Neglecting disk friction, 
journal friction, and leakage, the efficiency of the pump can be found 
in the same way as that of- turbines (§ 186). Let M be the moment 
of the couple rotating the pump, and a its angular velocity; i»„ r„ 
the tangential velocity of the water and radius at the outlet 
surface; iw, n the same quantities at the inlet surface. Q being 
the discharge per second, the change of angular momentum per 
second is 

(GQ/g)(w.r„-«iiri). 
Hence M = (GQ/g) (tp„r„ — Win). 

In normal working, «i» = o. Also, multiplying by the angular velocity, 
the work done per second is 

Ma = {GQIg)w a r a. 

But the useful work done in pumping is GQH. Therefore the 
efficiency is 

,, =GQH/Ma =gH/Kv„a =gH/wM . (7) 

§ 209. Case 1. Centrifugal Pump with no Whirlpool Chamber. — 
When no special provision is made to utilize the energy of motion of 
the water leaving the wheel, and the pump discharges directly into a 
chamber in which the water is flowing to the discharge pipe, nearly 
the whole of the energy of the water leaving the disk is wasted. The 
water leaves the disk with the more or less considerable velocity v , 
and impinges on a mass flowing to the discharge pipe at the much 
slower velocity v,. The radial component of v is almost necessarily 
wasted. From the tangential component there is a gain of pressure 

(«>„ 2 — l> s 2 )/2g— (w„ — fl s ) 2 /2g 
= V,(W — V.)[g, 

which will be small, if v, is small compared with iv . Its greatest 
value, if v, =!jWo, is \wJ-\2g, which will always be a small part of the 
whole head. Suppose this neglected. The whole variation of 
pressure in the pump disk then balances the lift and the head 
tti 2 /2g necessary to give the initial velocity of flow in the eye of the 
wheel. 

K.-^g+H =V„ 2 /2g-M„ 2 COSeC 2 </./2g+Mi 2 /2g, 

H=V//2g-«„ 2 cosec '<t>/2g} r (8) 

or V„ = V (2gH -\-Uo- cosec 2 $ . ) 

and the efficiency of the pump is, from (7), 

,=gH/V.w„=gH/{V(V„-»„cot0)), 
= (V«, 2 -«„ 2 cosec 2 <fr)/(2V (V„- Wo cot <t>\, (9) 

For<*>=90°, 77=(V„ 2 -m„ 2 )/2YV, 

which is necessarily less than J. That is, half the work expended in 
driving the pump is wasted. By recurving the vanes, a plan intro- 
duced by Appold, the efficiency is increased, because the velocity 
v, of discharge from the pump is diminished. If <#> is very small, 

cosec </> = cot <t> ; 
and then ij = (V„+w„ cosec *)/2V„, 

which may approach the value I, as <j> tends towards o. Equation 
(8) shows that u„ cosec 4> cannot be greater than V». Putting 
w„ =o - 25V (2gH) we S^t the following numerical values of the 
efficiency and the circumferential velocity of the pump:— 



PUMPS] 



HYDRAULICS 



109 



*o 


V 


9°! 


0-47 


45: 


0-56 


3°: 


0-65 


20° 


o-73 


IO° 


0-84 



v„ 

i-03V2gH 
1-06 „ 

I-I2 „ 

1-24 -, 

i-75 .. 

<t> cannot practically be made less than 20°; and, allowing for the 
frictional losses neglected, the efficiency of a pump in which <£ = 20° is 
found to be about -6o. 

§ 210. Case 2. Pump with a Whirlpool Chamber, as in fig. 210. — 
Professor James Thomson first suggested that the energy of the water 
after leaving the pump disk might be utilized, if a space were left 
in which a free vortex could be formed. In such a free vortex the 
velocity varies inversely as the radius. The gain of pressure in the 
vortex chamber is, putting r„, r„ for the radii to the outlet surface 
of wheel and to outside of free vortex, 



M-Sv-')- 



if k = rjr w . 

The lift is then, adding this to the lift in the last case, 

H = jV^-Mo 2 cosec 2 0+». s (i -* 2 )!/2£. 
But t , „ 2 =V 1 , 2 -2'V M o cot ip+Uo 1 cosec 2 -|>; 

.-.H = ((2 ~k r )V<?-2k\'oU cot 0-fc 2 tt o 2 cosec 2 4>|/2g. (10) 

Putting this in the expression for the efficiency, we find a con- 
siderable increase of efficiency. Thus with 

= 90° and k = i, v\ nearly, 

ij> a small angle and k — \, ij = I nearly. 

With this arrangement of pump, therefore, the angle at the outer 
ends of the vanes is of comparatively little importance. A moderate 
angle of 30 or 40 may very well be adopted. The following 
numerical values of the velocity of the circumference of the pump 

= 0-25V(2gH). 



have been obtained by taking k - 


= J, and «„ = ()• 


<t> 


V. 


90 


■762 V 2gH 


< 


•842 „ 


30 


•911 .. 


20° 


1-023 „ 



The quantity of water to be pumped by a centrifugal pump neces- 
sarily varies, and an adjustment for different quantities of water can- 
not easily be introduced. Hence it is that the average efficiency of 
pumps of this kind is in practice less than the efficiencies given above. 
The advantage of a vortex chamber is also generally neglected. The 
velocity in the supply and discharge pipes is also often made greater 
than is consistent with a high degree of efficiency. Velocities of 6 
or 7 ft. per second in the discharge and suction pipes, when the lift 
is small, cause a very sensible waste of energy; 3 to 6 ft. would 
be much better. Centrifugal pumps of very large size have been 
constructed. Easton and Anderson made pumps for the North Sea 
canal in Holland to deliver each 670 tons of water per minute on a 
lift of 5 ft. The pump disks are 8 ft. diameter. J. and H. Gwynne 
constructed some pumps for draining the Ferrarese Marshes, which 
together deliver 2000 tons per minute. A pump made under Pro- 
fessor J. Thomson's direction for drainage works in Barbados had 
a pump disk 16 ft. in diameter and a whirlpool chamber 32 ft. in 
diameter. The efficiency of centrifugal pumps. when delivering less 
or more than the normal quantity of water is discussed in a paper in 
the Proc. Inst. Civ. Eng. vol. 53. 

§ 211. High Lift Centrifugal Pumps. — It has long been known 
that centrifugal pumps could be worked in series, each pump 
overcoming a part of the lift. This method has been perfected, 
and centrifugal pumps for very high lifts with great efficiency 
have been used by Sulzer and others. C. W. Darley (Proc. Inst. 
Civ. Eng., supplement to vol. 154, p. 156) has described some 
pumps of this new type driven by Parsons steam turbines for 
the water supply of Sydney, N.S.W. Each pump was designed to 
deliver 1 5 million gallons per twenty-four hours against a head 
of 240 ft. at 3300 revs, per minute. Three pumps in series give 
therefore a lift of 720 ft. The pump consists of a central double- 
sided impeller 12 in. diameter. The water entering at the 
bottom divides and enters the runner at each side through a 
bell-mouthed passage. The shaft is provided with ring and 
groove glands which on the suction side keep the air out and on 
the pressure side prevent leakage. Some water from the pressure 
side leaks through the glands, but beyond the first grooves it 
passes into a pocket and is returned to the suction side of the pump. 
For the glands on the suction side water is supplied from a low- 
pressure service. No packing is used in the glands. During 
the trials no water was seen at the gk>nds. The following are 
the results of tests made at Newcastle:- - 



Duration of test . hours 

Steam pressure lb per sq. in. 
Weight of steam per water 

h.p. hour ft 

Speed in revs, per min. 
Height of suction . . .ft. 

Total lift ft. 

Million galls, per day pumped — 

By Ventun meter 

By orifice ..... 
Water h.p. ....... 



2 

57 

27-93 

3300 

11 

762 

1-573 
1-623 

252 



II. 



1-54 

57 

30-67 

3330 
11 

744 

1-499 
1-513 
235 



III. 



1-2 

84 

28-83 
3710 

II 
917 

1-689 
1-723 
326 



IV. 



1-55 
55 

27-89 

3340 

11 

756 

I-503 
1-555 
239 




Stand 
Pipe 



In trial IV. the steam was superheated 95° F. From other 
trials under the same conditions as trial I. the Parsons turbine 
uses 15-6 lb of steam per brake h.p. hour, so that the combined 
efficiency of turbine and pumps is about 56%, a remarkably 
good result. 

§ 212. Air-Lift Pumps.— -An interesting and simple method of 
pumping by compressed air, invented by Dr J. Pohle of Arizona, 
is likely to be Very useful in certain cases. Suppose a rising 
main placed in a deep bote hole in which there is a considerable 
depth of water. Air compressed to a sufficient pressure is con- 
veyed by an air pipe and introduced at the lower end of the rising 
main. The air 
rising in the main 
diminishes the 
average density 
of the contents of 
the main, and 
their aggregate 
weight no longer 
balances the pres- 
sure at the lower 
end of the main 
due to its sub- 
mersion. An up- 
ward flow is set 
up, and if the air 
supply is suffi- 
cient the water 
in the rising main 
is lifted to any Wg$0&g&$Pj 
required height. 
The higher the 
lift above the 
level in the bore 
hole the deeper 
must be the point 
at which air is 
injected. Fig. 
212 shows an air- 
lift pump con- 
structed for W. 
H. Maxwell at 
the Tunbridge 
Wells water- 
works. There is a 
two-stage steam 
air compressor, 
compressing air to 
from 90 to 100 lb 

per sq. in. The bore hole is 3 50 ft. deep, lined with steel pipes 1 5 in^" 
diameter for 200 ft. and with perforated pipes i3j.in. diameter for 
the lower 150 ft. The rest level of the water is 96 ft. from the 
ground-level, and the level when pumping 32,000 gallons per hour 
is 1 20 ft. from the ground-level. The rising main is 7 in. diameter, 
and is carried nearly to the bottom of the bore hole and to 
20 ft. above the ground-level. The air pipe is 25 in. diameter, 
In a trial run 31,402 gallons per hour were raised 133 ft. above 
the level in the well. Trials of the efficiency of the system made 
at San Francisco with varying conditions will be found in a 
paper by E. A. Rix (Journ. Amer. Assoc. Eng. Soc. vol. 25, 




I iffttSi 

U-Steel Tubes IS'piam. 
Main 7Diam. 



rfrrfi 
jilj 



Rising 

Air Pip* 2i' Dlam 



Fig. 212. 



no 



HYDRAZINE; 



1 900) . Maxwell found the best results when the ratio of immersion 
to lift was 3 to i at the start and 2-2 to 1 at the end of the trial. 
In these conditions the efficiency was 37% calculated Ori the 
indicated h.p. of the steam-engine, and 46% calculated on the 
indicated work of the compressor. 2-7 volumes of free air were 
used to 1 of water lifted. The system is suitable for temporary 
purposes, especially as the quantity of water raised is much 
greater than could be pumped by any other system in a bore 
hole of a given size. It is useful for clearing a boring of sand 
and may be advantageously used permanently when a boring 
is in sand or gravel which cannot be kept out of the bore hole. 
The initial cost is small. 

§ 213. Centrifugal Fans. — Centrifugal fans are constructed 
similarly ta centrifugal pumps, and are used for compressing 
air to pressures not exceeding 10 to 15 in. of water-column. 
With this small variation of pressure the variation of volume 
and density of the air may be neglected without sensible error. 
The conditions of pressure and discharge for fans are gener- 
ally less accurately known than in the case of pumps, and the 
design of fans is generally somewhat crude. They seldom have 
whirlpool chambers, though a large expanding outlet is pro- 
vided in the case of the important Guibal fans used in mine 
ventilation. 

It is usual to reckon the difference of pressure at the inlet 
and outlet of a fan in inches of water-column. One inch of water- 
column =64-4 ft. of air at average atmospheric pressure = 5-2lb per 
sq. ft. 

Roughly the pressure-head produced in a fan without means of 
utilizing the kinetic energy of discharge would be i s /2g ft. of air, or 
0-00024 u ! in. of water, where v is the velocity of the tips of thefan 
blades in feet per second. If d is the diameter of the fan and t the width 
at the external circumference, then ndt is the discharge area of the fan 
disk. If Q is the discharge in cub. ft. per sec, u =Q/xdi is the radial 
velocity of discharge which is numerically equal to the discharge per 
square foot of outlet in cubic feet per second. As both the losses in the fan 
and the work done are roughly proportional to m 2 in fans of the same 
type, and are also proportional to the gauge pressure p, then if the 
losses are to be a constant percentage of the work done u may be 
taken proportional to V P- In ordinary cases « = about 22V p. The 
width t of the fan is generally from 0-35 to o-45<2. Hence if Q is 
given, the diameter of the fan should be: — 

For/=o-35d, d=o-2oV(Q/V/>) 

For<=o-45<Z, <2=o-i8V (QH p) 

If p is the pressure difference in the fan in inches of water, and N the 
revolutions of fan, 

u=7r<2N/6o ft. per sec. 

N = i23oVf>/<2 <•■ revs, per n>in. 
As the pressure difference is small, the work done in compressing the 
air is almost exactly $-2pQ foot-pounds per second. Usually, however, 
the kinetic energy of the air in the discharge pipe is not inconsiderable 
compared with the work done in compression. If w is the velocity 
of the air where the discharge pressure is measured, the air carries 
away w t /2g foot-pounds per lb of air as kinetic energy. In Q cubic feet 
or o-o8o7QIb the kinetic energy is 0-00125 Qw 2 foot-pounds per 
second. 

The efficiency of fans is reckoned in two ways. If B.H.P, is the 
effective horse-power applied at the fan shaft, then the efficiency 
reckoned on the work of compression is 

>> = 5-2pQ/55oB.H.P. 
On the other hand, if the kinetic energy in the delivery pipe is taken 
as part of the useful work the efficiency is 

^ = (5-2£Q+a-ooi25Qa> 2 )/55oB.H.P. 
Although the theory above is a rough one it agrees sufficiently with 
experiment, with some merely numerical modifications. 

An extremely interesting experimental investigation of the action 
of centrifugal fans has been made by H. Heenan and W. Gilbert 
(Proc. Inst. Civ. Eng. vol. 123, p. 272). The fans delivered through an 
air trunk in which different resistances could be obtained by intro- 
ducing diaphragms with circular apertures of different sizes. Suppose 
a fan run at constant speed with different resistances and the com- 
pression pressure, discharge and brake horse-power measured. The 
results plot in such a diagram as is shown in fig. 213. The less the 
resistance to discharge, that is the larger the opening in the air trunk, 
the greater the quantity of air discharged at the given speed of the 
fan. On the other hand the compression pressure diminishes. The 
c*rve marked total gauge is the compression' pressure -(-the velocity 
head in the discharge pipe, both in inches of water,. This curve falls, 
but not nearly so much as the compression curve, when the resist- 
ance 13 the air trunk is diminished. The brake horse-power increases 
as tne resistance is diminished because the volume of discharge in- 
crease* very much. The curve marked efficiency is tile efficiency 



calculated on the work of compression only. It is zero for no dis- 
charge, and zero also when there is no resistance and all the energy 
given to the air is carried away as kinetic energy. There is a dis- 
charge for which this efficiency is a maximum ; it is about half the 
discharge which there is when there is no resistance and the delivery 
pipe is full open. The conditions of speed and discharge correspond- 
ing to the greatest efficiency of compression are those ordinarily 
taken as the best normal conditions of working. The curve marked 



«o 


*• 


ta- 


to 


e 


il- 








J 


i 


c 


* 


£ 


* 


1 


1 


V 






J; 


.6 


1 


«5» y* 


l- 




1 


«• 


J . 


0! 




3P00 
Discharge - C '.ft per min. 

Tip Speed * 100 ft. per sec. 

Fig. 213. • 

total efficiency gives the efficiency calculated on the work of com- 
pression and kinetic energy of discharge. Messrs Gilbert and 
Heenan found the efficiencies of ordinary fans calculated on the 
compression to be 40 to 60% when working at about normal 
conditions. 

Taking some, of Messrs Heenan and Gilbert's results for ordinary 
fans in normal conditions, they have been found to agree fairly with 
the following approximate rules. Let p c be the compression pressure 
and 5 the volume discharged per second per square foot of outlet area .of 
fan. . Then the total gauge pressure due to pressure of compression 
and velocity of discharge is approximately: p=p e +o-ooo±q 2 in. of 
water, so that if p c is given, p can be found approximately. The 
pressure p depends on the circumferential speed * of the fan disk — 

/► = 0-0O025f 2 in. oi water 

v = 63V P ft. per sec. 
The discharge per square foot of outlet of fan is — 

2 = 15 to i8Vp cub. ft. per sec. 
The total discharge is 

Q—Tdtq = 47 to 56 dHp 
For • ' = -35^. d = o-22 to o-25V(Q/V£) ft. 

/ = -45<f, d = o-2o to o-22V(Q/V» ft. 
N = 1203V pjd. 

These approximate equations, which are derived purely from 
experiment, do not differ greatly from those obtained by the rough 
theory given above. The theory helps to explain the reason for the 
form of the empirical results. (W. C. U.) 

HYDRAZINE (Diamidogen) , N 2 H 4 or H 2 N-NH 2 , a compound 
of hydrogen and nitrogen, first prepared by Th. Curtius in 1887 
from diazo-acetic ester, N 2 CH-C0 2 C 2 H 5 . This ester, which is 
obtained by the action of potassium nitrate on the hydrochloride 
of amidoacetic ester, yields on hydrolysis with hot concentrated 
potassium hydroxide an acid, which Curtius regarded as 
CsH 3 N<s(C0 2 H)3, but which A. Hantzsch and O. Silberrad 
(Ber., 1900, 33, p. 58) showed to be C 2 H 2 N4(C0 2 H) 2 , bisdiazo- 
acelic acid. On digestion of its warm aqueous solution witTl 
warm dilute sulphuric acid, hydrazine sulphate and oxalic acid 
are obtained. C. A. Lobry de Bruyn {Ber., 1895, 28, p. 3085) 
prepared free hydrazine by dissolving its hydrochloride in 
methyl alcohol and adding sodium methylate; sodium chloride 
was precipitated and the residual liquid afterwards fractionated 
under reduced pressure. It can also be prepared by reducing 
potassium dinitrososulphonate in ice cold water by means of 
sodium amalgam: — 



KSO, 



KSO 



™'>N-NO^^yf>N-NH 2 ^K 2 SO<+N,H 4 . 



HYDRAZONE^HYERQOBPHALUS 



in 



P. J. Schestakov (/. Smss. Phys. Chem. Sec.; 190$, 37, p. 1) 
obtained hydrazine by oxidizing urea with sodium hypochlorite 
in the presence of benzaldehyde, which, by combining with the 
hydrazine, protected it from oxidation. F. Raschig (German 
Patent 198307, 1908) obtained good yields by oxidizing ammonia 
with sodium hypochlorite in solutions made viscous with glue. 
Free hydrazine is a colourless liquid which boils at 113-5° C, 
and solidifies about o° C. to colourless crystals; it is heavier 
than water, in which it dissolves with' rise of temperature. It 
is rapidly oxidized on exposure, is a strong reducing agent, and 
reacts vigorously with the halogens. Under certain conditions 
it may be oxidized to azoimide (A. W, Browne and F. F. 
Shetterly, /. Amer. C.S., 1908, p. c^f By fractional distilla- 
tion of its aqueous solution hydrazine hydrate N2HVH2O 
(or perhaps H 2 N-NH»OH), a 'strong base, is obtained, which 
precipitates the metals from solutions of copper and silver 
salts at ordinary temperatures. It dissociates completely in a 
vacuum at 143°, and when heated under atmospheric pressure 
to 183 it decomposes into ammonia and nitrogen (A. Scott, 
/. Chem. Soc, 1904, 85, p. 913). The sulphate N2H<-H 2 S04, 
crystallizes in tables which are slightly soluble in cold water 
and readily soluble in hot water; it is decomposed by heating 
above 250 C. with explosive evolution of gas and liberation of 
sulphur. By the addition of barium chloride to the sulphate, a 
solution of the hydrochloride is obtained, from which the 
crystallized salt may be obtained on evaporation. 

Many organic derivatives of "hydrazine are known, the most 
important being phenylhydrazine^ which was discovered by Emil 
Fischer in 1877. It can be best prepared by V. Meyer and Lecco's 
method (Ber., 1883, 16, p. 2976), which consists in reducing phenyl- 
diazonium chloride in concentrated.hydrochloric acid, solution With 
stannous chloride also dissolved in, concentrated hydrochloric acid. 
Phenylhydrazine is liberated from the hydrochloride so obtained 
by adding sodium hydroxide, the solution being then extracted With 
ether, the ether distilled off, and the residual oil purified by distilla- 
tion under reduced pressure. Another method is, due to 13, Bam- 
berger. The diazonium chloride, by the addition of an alkaline 
sulphite, is converted into a diazosulphonate, which is then reduced 
by zinc dust and acetic acid to phenylhydrazine potassium sulphite. 
This salt is then hydrolysed by heating it with hydrochloric acid — 

C 6 H 5 XjCl + K 2 SO s = KC1 + C 6 H 6 NrSO s K, 
C 6 H 5 N,-S0 3 K + 2H = C 6 H 5 -NH-NH-S0 3 K, • 
C,H S NH-NHS0 3 K+HC1+ H20 = C,,H s -NHNH^Ha-f KHSO^. 

Phenylhydrazine is a colourless oily liquid which turns brown On 
exposure. It boils at 241 ° C, and melts at I7-5" G. It is slightly 
soluble in water, and is strongly basic, forming well-defined salts 
with acids. For the detection of substances containing- the carbonyl 
group (such for example as aldehydes and ketones) phenylhydrazine 
is a very important reagent, since it combines with them with 
elimination of water and the formation of well-defined hydrazines 
(see Aldehydes, Ketones and Sugars). It is a strong reducing 
agent; it precipitates cuprous oxide when heated , with FefUing's 
solution, nitrogen and benzene beiiig formed at the same time — 
C 6 H,NH-NH 2 + 2CuO ^CujO+Nj+riiO+CsIV By energetic re- 
duction of phenylhydrazine {e.g. by use of zisc dust ahd hydrochloric 
acid), ammonia and aniline are produced— C 6 H5NH-MHi + 2H * 
CjHjNHj + NH». It is also a most Important synthetic reagent, 
1 1 combines with aceto-acetic ester to form phfenylrnethyilpyrazolone' 
from which antipyrine {q.v.) may be obtained. Indoles (q.v.) are 
formed by heating certain hydrazones with anhydrous zinc chloride; 
while semicarbazides, pyrrols (q.v.) and many other types of organic 
compounds may be synthesized by the use of suitable phenylhydrazine 
derivatives. 

HYDRAZONE, in chemistry, a compound formed by the con- 
densation of a hydrazine with a cafbonyl group (see Alde- 
hydes ; Ketones). 

HYDROCARBON, in chemistry, a compound of carbon and 
hydrogen. Many occur in nature in the free state: for example, 
natural gas, petroleum and paraffin are entirely composed of 
such bodies; other natural sources are india-rubber, turpentine 
and certain essential oils. They are also revealed by the spectro- 
scope in stars, comets and the sun. Of artificial productions the 
most fruitful and important is prpvided by the destructive or 
dry distillation of many organic substances; familiar examples 
are the distillation of coal, which yields ordinary lighting gas, 
composed of gaseous hydrocarbofis, ' and also coal tar, which; 
on subsequent fractional distillations, yields many liquid and 



solid hydrocarbons, all of high industrial value. For details 
reference should be made to the articles wherein the above 
subjects- are treated. From the chemical point of view the 
hydrocarbons are of fundamental importance, and, on account 
of their great number, and still greater number of derivatives, 
they are studied as a separate branch of the science, namely, 
organic chemistry. 

See Chemistry for an account of their classification, &c. 
HYDROCELE (Gr. i&sop, water, and k^Xjj, tumour), the 
medical term for arty collection of fluid other than pus or blood 
in the neighbourhood of the testis or cord. The fluid is usually 
serous. " Hydrocele may be congenital or arise in the middle-aged 
withdut apparent cause, but it is usually associated with chronic 
orchitis or with tertiary syphilitic enlargements. The hydrocele 
appears as a. rbunded, fluctuating translucent swelling in the 
scrotum, and wheri greatly distended causes a dragging pain; 
Palliative treatment consists in tapping aseptically and remov- 
ing the ' fluid, the patient afterwards wearing a suspenderi 
The condition frequently recurs and necessitates radical 
treatment. Various substances may be injected; or the 
hydrocele is incised,' the tunica partly removed and the cavity 
drained. '■ 

HYDROCEPHALUS (Gr. iiBwp, water, and KG/poKr/, head), 
a term applied to disease of the brain which is attended 
with excessive effusion of fluid into its cavities. It exists 
in two forms— acute and chronic hydrocephalus. Acute hydro- 
cephalus is another- name for tuberculous meningitis (see 
Meningitis). 

Chronic hydrocephalus, or "water on the brain," consists in 
an effusion of fluid into the lateral ventricles of the brain. It 
is not preceded by tuberculous deposit or acute inflammation, 
but depends upon congenital malformation or upon chronic 
inflammatory changes affecting the membranes. When the 
disease is congenital, its presence in the foetus isapt to be a source 
of difficulty ' in parturition. It is however more commonly 
developed in" the first six months of life; but it occaskmally 
arises in older children, or even in adults. The chief symptom 
is the gradual increase in size of the upper part of the head out 
of all proportion to the face or the rest of the body. Occurring 
at an age when as yet the txjnes of the skull have not; become 
welded together, the enla*gement may go on to an enormous 
extent, the Spaces betweek -the bones becoming more and more 
expanded.' In a well-marked' case the deformity is very striking; 
the tippet part of the forehead projects abnormally, and the 
orbital plates of the frontal bone being inclined forwards give 
a dd torn ward- tilt to the eyes, which have also peculiar rolling 
movements. The face is small, and this, with the enlarged head, 
gives' a- remarkable aged expression to the child. The body is 
illinoufisried; the bones are thin, the hair is scanty and fine and 
the teeth 'carious or absent. . ; 

The average circumference of* the adult head' is 22 in v - and in 
the normal child it is of course much less. In chronic hydro- 
cephalus the'head of an infant three months old has measured 
29 in.; and in the* case of the man Cardinal, who died in Guy's 
Hospital'/the head measured 33 in. In such cases the head 
cannot be supported by the neck, and the patient has to keep 
mostly in the recumbent posture. The expansibility of the skull 
prevents destructive pressure on the brain, yet this organ is 
materially affected by the presence of the fluid. The cerebral 
ventricles are distended, and the convolutions are flattened, 
OCcasidnally the fluid escapes into the cavity of the cranium, 
which it fills, pressing down the brain to the base of the skull. ~ 
As a consequence, the functions of the brain are interfered 
with, and the 1 inefital condition is impaired. The child is dull, 
listless arid irritable, and sometimes imbecile. The special senses 
bfecbme affected as the disease advances; sight is often lost, as 
is also hearing. Hydrocephalic children generally sink in a few 
years;' nevertheless there have been instances of persons with 
this disease living to old age. There are, of course, grades of the 
affection; and children may present many of the symptoms of 
it in a slight degree, and yet recover, the head ceasing to expand, 
and becoming in due course" firmly ossified. 



112 



HYDR0CHARI0EAE 



Various methods of treatment have been employed, but the 
results are unsatisfactory. Compression of the head by bandages, 
and the administration of mercury with the view of promoting 
absorption of the fluid, are now little resorted to. Tapping the 
fluid from time to time through one of the spaces between the 
bones, drawing off a little, and thereafter employing gentle 
pressure, has been tried, but rarely with benefit. Attempts have 
also been made to establish a permanent drainage between the 
interior of the lateral ventricle and the sub-dura! space, tod 
between the lumbar region of the spine and the abdomen, but 
without satisfactory results. On the whole, the plan Of treatment 
which aims at maintaining the patient's nutrition by appropriate 
food and tonics is the most rational and successful. (E. O.*) 

HYDROCHARIDEAE, in botany, a natural order of Mono- 
cotyledons, belonging to the series Helobieae. They are water- 
plants, represented in Britain by frog-bit {Hydrocharis Morsus- 
ranae) and water-soldier (Stratiotes alotdes). The order contains 
about fifty species in fifteen genera, twelve of which occur in 
fresh water while three are marine: and includes both floating 

and submerged forms. 
Hydrocharis floats on 
the surface of still 
water, andh*s rosettes 
of kidney-shaped 
leaves, from among 
which spring the 
flower-stalks; stolons 
bearing new leaf- 
rosettes are sent out 
on all sides, the plant 
thus propagating itself 
in the same way as 
the strawberry. 
Stratiotes alotdes has a 
rosette of stiff sword- 
like leaves, which when 
the plant is in flower 
project above the 
surface; it is also 
stoloniferous, the 
young rosettes sinking 
to the bottom at the 
beginning of winter 
and rising again to the 
surface in the spring. 
Vallisneria (eel-grass) 
contains two species, 
one native of tropical 
Asia, the other, in- 
habiting the wanner 
parts of both hemi- 
spheres and reaching 
as far north as south 
Europe. It grows in 
the mud at the bottom 
of fresh water, and the 
short stem bears a 
cluster of long, narrow 
grass-like leaves; new 
plants are formed at 




Morsus-ranae — 



Fig. i. — Hydrocharis 
Frog-bit — male plant. 

1, Female flower. 

2, Stamens, enlarged. 

3, Barren pistil of male flower, enlarged. 

4, Pistil of female flower. 

5, Fruit. 

6, Fruit cut transversely. 

I) 9. Floral diagrams of male and female * he end f Iwfkontai 
flowers respectively. runners. Another type 

s, Rudimentary stamens. is represented by 

Elodea canadensis or 
water-thyme, which has been introduced into the British Isles from 
North America. It is a small, submerged plant with long, slender 
branching stems bearing whorls of narrow toothed leaves; the 
flowers appear at the surface when mature. Halophila, Enhalus 
and Thalassia are submerged maritime plants found on trppical 
coasts, mainly in the Indian and Pacific oceans; Halophila has 
an elongated stem rooting at the nodes; Enhalus a short, thick 
rhizome, clothed with black threads resembling horse-hair, the 



persistent hard-bast strands of the leaves; Thalassia has a 
creeping rooting stem with upright branches bearing crowded 
strap-shaped leaves in two rows. The flowers spring from, or are 
enclosed in, a spathe, and are unisexual and regular, with 
generally a calyx and corolla, each of three members; the 
stamens are in whorls of three, the inner whorls are often barren; 
the two to fifteen carpels form an inferior ovary containing 
generally numerous ovules on often large, produced, parietal 
placentas. The fruit is leathery or fleshy, opening irregularly. 
The seeds contain a large embryo and no endosperm. In 
Hydrocharis (fig. 
i), which is dioe- 
cious, the flowers 
are borne above 
the surface of the 
water, have con- 
spicuous white 
petals, contain 
honey and are 
pollinated by in- 
sects. Stratiotes 
has similar flowers 
which come above | 
the surface only 
for pollination, 
becoming sub- 
merged again 
during ripening of 
the fruit. In Val- 
lisneria (fig. 2), 
which is also dioe- 
cious, the small 
male flowers are 
borne in large 
numbers in short- 
stalked spathes; 
the petals are 
minute and scale- 
like, and only two 
of the three 
stamens are fer- 




Fig. 



spiralis — Eel grass — 
A, Female plant; B, 



_ _ 2. — Vallisneria 

tile; the flowers ^ bo . ut \ natural size - 
, ' , . , , Male plant, 

become detached r 

before opening and rise to the surface, where the sepals expand 
and form a float bearing the two projecting semi-erect stamens. 
The female flowers are solitary and are raised to the surface 
on a long, spiral stall:; the ovary bears three broad styles, on* 
which some of the 
large, sticky 
pollen-grains from 
the floating male 
flowers get de- 
posited (fig. 3). 
After pollination 
the female flower 
becomes drawn 
below the surface 
by the spiral con- 
traction of the 
long stalk, and the 
fruit ripens near 
the bottom. 
Elodea has poly- 
gamous flowers 




Fig. 3. 



(that is, male, female and hermaphrodite), solitary, in slender, 
tubular spathes; the male flowers become detached and rise to 
the surface; the females are raised to the surface when mature, 
and receive the floating pollen from the male. The flowers of 
Halophila are submerged and apetalous. 

The order is a widely distributed one; the marine forms are 
tropical or subtropical, but the fresh- water genera occur also in 
the temperate zones. 



HYDROCHLORIC ACID— HYDROGEN 



113 



HYDROCHLORIC ACID, also known in commerce as " spirits 
of salts " and " muriatic acid," a compound of hydrogen and 
chlorine. Its chemistry is discussed under Chlorine, and its 
manufacture under Alkali Manufacture. 

HYDRODYNAMICS (Gr. vScop, water, dvuatus, strength), 
the branch of hydromechanics which discusses the motion of 
fluids (see Hydromechanics). 

HYDROGEN [symbol H, atomic weight 1-008 (0=16)], one 
of the chemical elements. Its name is derived from Gr. vdup, 
water, and yevvauv, to produce, in allusion to the fact that 
water is produced when the gas burns in air. Hydrogen appears 
to have been recognized by Paracelsus in the 16th century; 
the combustibility of the gas was noticed by Turquet de Mayenne 
in the 17th century, whilst in 1700 N. Lemery showed that a 
mixture of hydrogen and air detonated on the application of 
a light. The first definite experiments concerning the nature 
of hydrogen were made in 1766 by H. Cavendish, who showed 
that it was formed when various metals were acted upon by 
dilute sulphuric or hydrochloric acids. Cavendish called it " in- 
flammable air," and for some time it was confused with other 
inflammable gases, all of which were supposed to contain the 
same inflammable principle, " phlogiston," in combination 
with varying amounts of other substances. In 1781 Cavendish 
showed that water was the only substance produced when 
hydrogen was burned in air or oxygen, it having been thought 
previously to this date that other substances were formed 
during the reaction, A. L. Lavoisier making many experiments 
with the object of finding an acid among the products of 
combustion. 

Hydrogen is found in the free state in some volcanic gases, in 
fumaroles, in the carnallite of the Stassfurt potash mines (H. 
Precht, Ber., 1886, 19, p. 2326), in some meteorites, in certain 
stars and nebulae, and also in the envelopes of the sun. In 
combination it is found as a constituent of water, of the gases 
from certain mineral springs, in many minerals, and in most 
animal and vegetable tissues. It may be prepared by the electro- 
lysis of acidulated water, by the decomposition of water by 
various metals or metallic hydrides, and by the action of many 
metals on acids or on bases. The alkali metals and alkaline earth 
metals decompose water at ordinary temperatures; magnesium 
begins to react above 70° C, and zinc at a dull red heat. The 
decomposition of steam by red hot iron has been studied by 
H. Sainte-Claire Deville (Comptes renins, 1870, 70, p. 1105) 
and by H. Debray (ibid., 1879, 88, p. 1341), who found that at 
about 1500 C. a condition of equilibrium is reached. H. Moissan 
(Bull. soc. chim., 1902, 27, p. 1 141) has shown that potassium 
hydride decomposes cold water, with evolution of hydrogen, 
KH + H 2 = KOH + H 2 . Calcium hydride or by drolite, prepared 
by passing hydrogen over heated calcium, decomposes water 
similarly, 1 gram giving 1 litre of gas; it has been proposed 
as a commercial source (Prats Aymerich, Abst. J.C.S., 1907, ii. 
p. 543), as has also aluminium turnings moistened with potassium 
cyanide and mercuric chloride, which decomposes water regularly 
at 70 , 1 gram giving 1-3 litres of gas (Mauricheau-Beaupre, 
Comptes rendus, 1908, 147, p. 310). Strontium hydride behaves 
similarly. In preparing the gas by the action of metals on 
acids, dilute sulphuric or hydrochloric acid is taken, and the 
metals commonly used are zinc or iron. So obtained, it contains 
many impurities, such as carbon dioxide, nitrogen, oxides of 
nitrogen, phosphoretted hydrogen, arseniuretted hydrogen, &c, 
the removal of which is a matter of great difficulty (see E. W. 
Morley, Amcr. Chem. Journ., 1890, 12,'p. 460). When prepared 
by the action of metals on bases, zinc or aluminium and caustic 
soda or caustic potash are used. Hydrogen may also be obtained 
by the action of zinc on ammonium salts (the nitrate excepted) 
(Lorin, Comptes rendus, 1865, 60, p. 745) and by heating 
the alkali formates or oxalates with caustic potash or soda, 
Na J C 2 0-4-r-2NaOH = H 2 +2Na 2 C0 3 . Technically it is prepared 
by the action of superheated steam on incandescent coke (see 
F. Hembert and Henry, Comptes rendus, 1885, 101, p. 797; 
A. Naumann and C. Pistor, Ber., 1885, 18, p. 1647), or by the 
electrolysis of a dilute solution of caustic soda (C. Winssinger, 



Chem. Zeit., 1898, 22, p. 609; " Die Elektrizitats-Aktiengesell- 
schaft," Zeit. f. Elektrochem., 1901, 7, p. 857). In the latter 
method a 15 % solution of caustic soda is used, and the 
electrodes are made of iron; the cell is packed in a wooden 
box , surrounded with sand, so that the temperature is kept 
at about 70 C; the solution is replenished, when necessary, 
with distilled water. The purity of the gas obtained is about 
97 % 

Pure hydrogen is a tasteless, colourless and odourless gas of 
specific gravity 0-06947 (air= 1) (Lord Rayleigh, Proc. Roy. Soc., 
1893, p. 319). It may be liquefied, the liquid boiling at -252-68° 
C. to -252-84°C, and it has also been solidified, the solid melting 
at -264° C. (J. Dewar, Comptes rendus, 1899, 129, p. 451; 
Chem. News, 1901, 84, p. 49; see also Liquid Gases). The 
specific heat of gaseous hydrogen (at constant pressure) is 
3.4041 (water=i), and the ratio of the specific heat at constant 
pressure to the specific heat at constant volume is 1-3852 (W. C. 
Rontgen, Pogg. Ann., 1873, 148, p. 580). On the spectrum see 
Spectroscopy. Hydrogen is only very slightly soluble in water. 
It diffuses very rapidly through a porous membrane, and through 
some metals at a red heat (T. Graham, Proc. Roy. Soc, 1867, 15, 
p. 223; H. Sainte-Claire Deville and L. Troost, Comptes rendus, 
1863, 56, p. 977). Palladium and some other metals are capable 
of absorbing large volumes of hydrogen (especially when the metal 
is used as a cathode in a water electrolysis apparatus). L. Troost 
and P. Hautefeuille (Ann. chim. phys., 1874, (5) 2, p. 279) 
considered that a palladium hydride of composition Pd 2 H was 
formed, but the investigations of C. Hoitsema (Zeit. phys. Chem., 
1895, 17, p. 1), from the standpoint of the phase rule, do not 
favour this view, Hoitsema being of the opinion that the occlusion 
of hydrogen by palladium is a process of continuous absorption. 
Hydrogen burns with a pale blue non-luminous flame, but will 
not support the combustion of ordinary combustibles. It forms 
a highly explosive mixture with air or oxygen, especially when in 
the proportion of two volumes of hydrogen to one volume of 
oxygen. H. B. Baker (Proc. Chem. Soc, 1902, 18, p. 40) has 
shown that perfectly dry hydrogen will not unite with perfectly 
dry oxygen. Hydrogen combines with fluorine, even at very low 
temperatures, with great violence; it also combines with carbon, 
at the temperature of the electric arc. The alkali metals when 
warmed in a current of hydrogen, at about 360° C, form hydrides 
of composition RH(R = Na, K, Rb, Cs), (H. Moissan, Bull. soc. 
chim., 1902, 27, p. 1 141); calcium and strontium similarly 
form hydrides CaH 2 , SrH 2 at a dull red heat (A. Guntz, Comptes 
rendus, 1901, 133, p. 1209). Hydrogen is a very powerful re- 
ducing agent; the gas occluded by palladium being very 
active in this respect, readily reducing ferric salts to 
ferrous salts, nitrates to nitrites and ammonia, chlorates to 
chlorides, &c. 

For determinations of the volume ratio with which hydrogen and 
oxygen combine, see J. B. Dumas, Ann. chim. phys., 1843 (3), 8, 
p. 189; O. Erdmann [and R. F. Marchand, ibid. p. 212; E. H. 
Keiser, Ber., 1887, 20, p. 2323; J. P. Cooke and T. W. Richards, 
Amer. Chem. Journ., 1888, 10, p. 191; Lord Rayleigh, Chem. News, 
1889, 59, p. 147; E. W. Morley, Zeit. phys. Chem., 1890, 20, p. 417; 
and S. A. Leduc, Comptes rendus, 1899, 128, p. 1158. 

Hydrogen combines with oxygen to form two definite com- 
pounds, namely, water (q.v.), H 2 0, and hydrogen peroxide, 
H 2 2 , whilst the existence of a third oxide, ozonic acid, has been 
indicated. 

Hydrogen peroxide, H2O2, was discovered by L. J. Thenard in 
187.8 (Ann. chim. phys., 8, p. 306). It occurs in small quantities 
in the atmosphere. It may be prepared by passing a currentof 
carbon dioxide through ice-cold water, to which small quantities 
of barium peroxide are added from time to time (F. Duprey, 
Comptes rendus, 1862, 55, p. 736; A. J. Balard, ibid., p. 758), 
Ba0 2 -fC0 2 +H 2 = H 2 2 +BaC0 3 . E. Merck (Abst. J.C.S., 
1907, ii., p. 859) showed that barium percarbonate, BaC0 4 , is 
formed when the gas is in excess; this substance readily yields 
the peroxide with an acid. Or barium peroxide may be decom- 
posed by hydrochloric, hydrofluoric, sulphuric or silicofluoric 
acids (L. Crismer, Bull. soc. chim., 1891 (3), 6, p. 24; Hanriot, 
Comptes rendus, 1885, 100, pp. 56, 172), the peroxide being added 



ii4 



HYDROGRAPHY— HYDROLYSIS 



in small quantities to a cold dilute solution of the acid. It is 
necessary that it should be as pure as possible since the commercial 
product usually contains traces of ferric, manganic and aluminium 
oxides, together tvith some silica. To purify the oxide, it is 
dissolved in dilute hydrochloric acid until the acid is neatly 
neutralized, the solution is cooled, filtered, and baryta water is 
added until a faint permanent white precipitate of hydrated 
barium peroxide appears; the solution is now filtered, and a 
concentrated solution of baryta water is added to the filtrate, 
when a crystalline precipitate of hydrated barium peroxide, 
Ba0 2 8-H 2 0, is thrown down. This is filtered off and well washed 
with water. The above methods give a dilute aqueous solution 
of hydrogen peroxide, which may be concentrated somewhat 
by evaporation over sulphuric acid in vacuo. H. P. Talbot and 
H. R. Moody (Jour. Anal. Chem., 1892, 6, p. 650) prepared a more 
concentrated solution from the commercial product, by the 
addition of a 10% solution of alcohol and baryta water. The 
solution is filtered, and the barium precipitated by sulphuric 
acid. The alcohol is removed by distillation in vacuo, and by 
further concentration in vacuo a solution may be obtained which 
evolves 580 volumes of oxygen. R. Wolffenstein (Ber., 1804, 
27, p. 2307) prepared practically anhydrous hydrogen peroxide 
(containing 99-x% H 2 2 ) by first removing all traces of dust, 
heavy metals and alkali from the commercial 3 % solution. 
The solution is then concentrated in an open basis on the water- 
bath until it contains 48% H2O2. The liquid so obtained is 
extracted with ether and the ethereal solution distilled under 
diminished pressure, and finally purified by repeated distillations. 
W. Staedel (Zeit. f. angew* Chem., 1902, 15, p. 642) has described 
solid hydrogen peroxide, obtained by freezing concentrated 
solutions. 

Hydrogen peroxide is also found as a product in many chemical 
actions, being formed when carbon monoxide and cyanogen burn 
in air (H. B. Dixon); by passing air through solutions of strong 
bases in the presence of such metals as do not react with the 
bases to liberate hydrogen; by shaking zinc amalgam with 
alcoholic sulphuric acid and air (M. Traube, Ber., ' t$82, 15, 
p. 659); in the oxidation of zinc, lead and copper 5 in presence of 
water, and in the electrolysis of sulphuric acid of such strength 
that it contains two molecules of water to one molecule of 
sulphuric acid (M. Berthelot, Comptcs rendus, 1878s 86, 
p. 71). ■ ■ ■ 

The anhydrous hydrogen peroxide obtained by Wolffenstein 
boils at 84-8 5°C. (68 mm.); its specific gravity is 1-4996 (1-5° C). 
It is very explosive (W. Spring, Zeit. anmg. Chem.j 1895, 8, 
p. 424). The explosion risk seems to be most marked in the 
preparations which have been extracted with ether previous to 
distillation, and J. W. Bruhl (Ber., 1895, 28, p. 2847) is of opinion 
that a very unstable, more highly oxidized product is produced 
in small quantity in the process. The solid variety prepared by 
Staedel forms colourless, prismatic crystals which melt at -2° C; 
it is decomposed with explosive violence by platinum sponge, and 
traces of manganese dioxide. , The dilute aqueous solution is 
very unstable, giving up oxygen readily, and decomposing with 
explosive violence at 100° C. An aqueous solution containing 
more than 1-5% hydrogen peroxide reacts slightly acid. To- 
wards lupetidin [aa' dimethyl piperidine, C 5 H 9 N(CHa)2l hydrogen 
peroxide acts as a dibasic acid (A. Marcuse and R. Wolffenstein, 
Ber., 1901, 34, p. 2430; see also G. Bredig, Zeit. Electrochem., 
1 901, 7, p. 622). Cryoscopic determinations of its molecular 
weight show that it is H2O2. [G. Carrara, Rend, delta Accad. 
dei Lincei, 1892 (5), 1, ii. p; 19; W. R. Orndorff and J. White, 
Amer. Chem. Journ., 1893, 15, p. 347.] Hydrogen peroxide 
behaves very frequently as a powerful oxidizing agent; thus 
lead sulphide is converted into lead sulphate in presence of a 
dilute aqueous solution of the peroxide, the hydroxides of the 
alkaline earth metals are converted into peroxides of the type 
MCV8H2O, titanium, dioxide is converted into the trioxide, 
iodiae is liberated from potassium iodide, and nitrites (in alkaline 
solution) are converted into acid-amides (B. Radziszewski,Ber., 
1884, .iii, p: 355). In many cases it is found that hydrogen 
peroxide will 'only act as an oxidant when in the presence of a 



catalyst; for example, formic, glygollic, lactic, tartaric, malic, 
benzoic and other organic acids are readily oxidized in the 
presence of ferrous sulphate (H. J. H. Fenton, Jour. Chem. Soc, 
1900, 77, p. 69), and sugars are readily oxidized in the presence 
of ferric chloride (O. Fischer and M. Busch, Ber., 1891, 24, 
p. 187 1). It is sought to explain these oxidation processes by 
assuming that the hydrogen peroxide unites with the compound 
undergoing oxidation to form an addition compound, which 
subsequently decomposes (J. H. Kastle and A. S. Loevenhart, 
Amer. Chem. Journ., 1903, 29, pp. 397, 517). Hydrogen peroxide 
can also react as a reducing agent, thus silver oxide is reduced 
with a rapid evolution of oxygen. The course of this reaction can 
scarcely be considered as definitely settled; M. Berthelot 
considers that a higher oxide of silver is formed, whilst A. 
Baeyer and V. Villiger are of opinion that reduced silver is 
obtained [see Comptes rendus, 1001, 133, p. 555; Ann. Chim. 
Phys., 1897 (7), 11, p. 217, and Ber., 1901, 34, p. 2769]. Potassium- 
permanganate, in the presence of dilute sulphuric acid, is rapidly 
reduced by hydrogen peroxide, oxygen being given off, 2KM„0 4 + 
3H 2 S04+5Hj>0 2 = KoS04-f-2MhS04+8H 2 0+502. Lead peroxide 
is reduced to the monoxide. Hypochlorous acid and its salts, 
together with the corresponding bromine and iodine compounds, 
liberate oxygen violently from hydrogen peroxide, giving hydro- 
chloric, hydrobromic and hydriodic acids (S. Tanatar, Ber., 1899, 
32, p. 1013). 

On the constitution of hydrogen peroxide see C. F. Schonbein, 
Jour, pritk. Chem., 1858-1868; M. Traube, Ber., 1882-1889; J. W. 
Bruhl, Ber<; 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, Ber., 

1903, 36. P- I893-. . . . 

Hydrogen peroxide finds application as a bleaching agent, as an 
antiseptic, for the removal of tne last traces of chlorine and sulphur 
dioxide employed in bleaching, and for various quantitative separa- 
tions in analytical chemistry. (P. Jannasch, Ber., 1893, 26, p. 2908). 
It may be estimated. by titration with potassium permanganate in 
acid solution; wjth potassium ferricyanide. in alkaline solution, 
2K 3 Fe(CN) 6 -|-2KOH-l-H 2 02=2K4Fe(CN)6-(-2H20+0 2 ;or by oxidiz- 
ing arsenious acid in alkaline solution with the peroxide and 
back- titration of the excess of arsenious acid with standard iodine 
(B. Grutzner, Arch, der Pharm., 1899, 237, p^ 705). It may be 
recognized by the violet coloration it gives when added to a very 
dilute solution of potassium bichromate in the presence of hydro- 
chloric acid; by the orange-red colour it gives with a solution of 
titanium dioxide in concentrated sulphuric acid ; and by the pre- 
cipitate of Prussian blue formed when it is added to a solution 
containing ferric chloride and potassium ferricyanide. 

Ozonic Acid, H2O4. By the action of ozone on a 40% solution 
of potassium hydroxide, placed in a freezing mixture, an orange- 
brown substance is obtained, probably K2O4, which A. Baeyer and 
V. Villiger [Ber., 1902, 35, p. 3038) think is derived from ozonic 
acid, produced according to the reaction O3 + H2O = H 2 4 . 

HYDROGRAPHY (Gr. vSup, water, and -ypd^eip, to write), 
the science dealing with all the waters of the earth's surface, 
including the description of their physical features and con- 
ditions; the preparation of charts andmaps showing the position 
of lakes, rivers, seas and oceans, the contour of the sea-bottom, 
the position of shallows, deeps, reefs and the direction and 
volume of currents; a scientific description of the position, 
volume, configuration, motion and condition of all the waters 
of the earth. See also Surveying (Nautical) and Ocean and 
Oceanography. The Hydrographic Department of the British 
Admiralty, established in 1795, undertakes the making of charts 
for the admiralty, and is under the charge of the hydrographer to 
the admiralty (see Chart). 

HYDROLYSIS (Gr. tiBoip, water, \vei.v, to loosen), in chemistry, 
a decomposition brought about by water after the manner shown 
in the equation R-X+H'OH = R-H+X-OH. Modern research 
has proved that such reactions are not occasioned by water 
acting as H 2 0, but really by its ions (hydrions and hydroxidions), 
for the velocity is proportional (in accordance with the law of 
chemical mass action) to the concentration of these ions. This 
fact explains the so-called " catalytic " action of acids and bases 
in decomposing such compounds as the esters. The term 
" saponification " (Lat. sapo, soap) has the same meaning, but 
it is more properly restricted to the hydrolysis of the fats, i.e. 
glyceryl esters of organic acids, into glycerin and a soap (see 
Chemical Action). 



HYDROMECHANICS 



1 5 



HYDROMECHANICS (Gr. v5poy.rixa.VLKa.), the science of the 
mechanics of water and fluids in general, including hydrostatics 
or the mathematical theory of fluids in equilibrium, and hydro- 
mechanics, the theory of fluids in motion. The practical applica- 
tion of hydromechanics forms the province of hydraulics (q.v.). 

Historical. — The fundamental principles of hydrostatics were first 
given by Archimedes in his work Ilepi w oxovixivuv, or De iis quae 
vehuntur in humido, about 250 B.C., and were afterwards applied 
to experiments by Marino Ghetaldi (1566-1627) in his Promotus 
Archimedes (1603). Archimedes maintained that each particle of 
a fluid mass, when in equilibrium, is equally pressed in every direc- 
tion ; and he inquired into the conditions according to which a solid 
body floating in a fluid should assume and preserve a position of 
equilibrium. 

In the Greek school at Alexandria, which flourished under the 
auspices of the Ptolemies, the first attempts were made at the 
construction of hydraulic machinery, and about 120 B.C. the fountain 
of compression, the siphon, and the forcing-pump were invented by 
Ctesibius and Hero. The siphon is a simple instrument; but the 
forcing-pump is a complicated invention, which could scarcely 
have been expected in the infancy of hydraulics. It was probably 
suggested to Ctesibius by the Egyptian Wheel or Noria, which was 
common at that time, and which was a kind of chain pump, con- 
sisting of a number of earthen pots carried' round by a wheel. In 
some of these machines the pots have a valve in the bottom which 
enables them to descend without much resistance, and diminishes 
greatly the load upon the wheel ; and, if we suppose that this valve 
was introduced so early as the time of Ctesibius, it is not difficult 
to perceive how such a machine might have led to the invention of 
the forcing-pump. 

Notwithstanding these inventions of the Alexandrian school, its 
attention does not seem to have been directed to the motion of 
fluids; and the first attempt to investigate this subject was made 
by Sextus Julius Frontinus, inspector of the public fountains at 
Rome in the reigns of Nerva and Trajan. In his work De aquae- 
ductibus urbis Romae commentarius , he considers the methods 
which were at that time employed for ascertaining the quantity of 
water discharged from ajutages, and the mode of distributing the 
waters of an aqueduct or a fountain. He remarked that the flow of 
water from an orifice depends not only on the magnitude of the orifice 
itself, but also on the height of the water in the reservoir; and that 
a pipe employed to carry off a portion of water from an aqueduct 
should, as circumstances required, have a position more or less 
inclined to the original direction of the current. But as he was 
unacquainted with the law of the velocities of running water as 
depending upon the depth of the orifice, the want of precision which 
appears in his results is not surprising. 

Benedetto Castelli (1577-1644), and Evangelista Torricelli (1608- 
1647), two of the disciples of Galileo, applied the discoveries of their 
master to the science of hydrodynamics. In 1628 Castelli published 
a small work, Delia misura dell' acque correnti, in which he satis- 
factorily explained several phenomena in the motion of fluids in 
rivers and canals; but he committed a great paralogism in sup- 
posing the velocity of the water proportional to the depth of the 
orifice below the surface of the vessel. Torricelli, observing that in 
a jet where the water rushed through a small ajutage it rose to nearly 
the same height with the reservoir from which it was supplied, 
imagined that it ought to move with the same velocity as if it had 
fallen through that height by the force of gravity, and hence he 
deduced the proposition that the velocities of liquids are as the 
square root of the head, apart from the resistance of the air and the 
friction of the orifice. This theorem was published in 1643, at the 
end of his treatise De motu gravium projectorum, and it was con- 
firmed by the experiments of Raffaello Magiotti on the quantities 
of water discharged from different ajutages under different pressures 
(1648). 

In the hands of Blaise Pascal (1623-1662) hydrostatics assumed 
the dignity of a science, and in a treatise on the equilibrium of 
liquids (Sur t'equilibre des liqueurs), found among his manuscripts 
after his death and published in 1663, the laws of the equilibrium 
of liquids were demonstrated in the most simple manner, and amply 
confirmed by experiments. 

The theorem of Torricelli was employed by many succeeding 
writers, but particularly by Edme Mariotte (1620-1684), whose 
Traiti du mouvement des eaux, published after his death in the year 
1686, is founded on a great variety of well-conducted experiments 
on the motion of fluids, performed at Versailles and Chantilly. In 
the discussion of some points he committed considerable mistakes. 
Others he treated very superficially, and in none of his experiments 
apparently did he attend to the diminution of efflux arising from the 
contraction of the liquid vein, when the orifice is merely a perforation 
in a thin plate ; but he appears to have been the first who attempted 
to ascribe the discrepancy between theory and experiment to the 
retardation of the water's velocity through friction. His contem- 
porary Domenico Guglielmini (1655-1710), who was inspector of 
the rivers and canals at Bologna, had ascribed this diminution of 
velocity in rivers to transverse motions arising from inequalities in 
their bottom. But as Mariotte observed similar obstructions even 
in glass pi[)es where no transverse currents could exist, the cause 



assigned by Guglielmini seemed destitute of foundation. The 
French philosopher, therefore, regarded these obstructions as the 
effects of friction. He supposed that the filaments of water which 
graze along the sides of the pipe lose a portion of their velocity; 
that the contiguous filaments, having on this account a greater 
velocity, rub upon the former, and suffer a diminution of their 
celerity; and that the other filaments are affected with similar 
retardations proportional to their distance from the axis of the pipe. 
In this way the medium velocity of the current may be diminished, 
and consequently the quantity of water discharged in a given time 
must, from the effects of friction, be considerably less than that 
which is computed from theory. 

The effects of friction and viscosity in diminishing the velocity of 
running water were noticed in the Principia of Sir Isaac Newton, 
who threw much light upon several branches of hydromechanics. 
At a time when the Cartesian system of vortices universally pre- 
vailed, he found it necessary to investigate that hypothesis, and in 
the course of his investigations he showed that the velocity of any 
stratum of the vortex is an arithmetical mean between the velocities 
of the strata which enclose it; and from this it evidently follows 
that the velocity of a filament of water moving in a pipe is an arith- 
metical mean between the velocities of the filaments which surround 
it. Taking advantage of these results, Henri Pitot (1695-1771) 
afterwards showed that the retardations arising from friction are 
inversely as the diameters of the pipes in which the fluid moves. 
The attention of Newton was also directed to the discharge of water 
from orifices in the bottom of vessels. He supposed a cylindrical 
vessel full of water to be perforated in its bottom with a small hole 
by which the water escaped, and the vessel to be supplied with 
water in such a manner that it always remained full at the same 
height. He then supposed this cylindrical column of water to be 
divided into two parts,— the first, which he called the " cataract," 
being an hyperboloid generated by the revolution of an hyperbola 
of the fifth degree around the axis of the cylinder which should pass 
through the orifice, and the second the remainder of the water in 
the cylindrical vessel. He considered the horizontal strata of this 
hyperboloid as always in motion, while the remainder of the water 
was in a state of rest, and imagined that there was a kind of cataract 
in the middle of the fluid. When the results of this theory were 
compared with the quantity of water actually discharged, Newton 
concluded that the velocity with which the water issued from the 
orifice was equal to that which a falling body would receive by 
descending through half the height of water in the reservoir. This 
conclusion, however, is absolutely irreconcilable with the known 
fact that jets of water rise nearly to the same height as their reservoirs, 
and Newton seems to have been aware of this objection. Accord- 
ingly, in the second edition of his Principia, which appeared in 1713, 
he reconsidered his theory. He had discovered a contraction in the 
vein of fluid {vena contractu) which issued from the orifice, and found 
that, at the distance of about a diameter of the aperture, the section 
of the vein was contracted in the subduplicate ratio of two to one. 
He regarded, therefore, the section of the contracted vein as the 
true orifice from which the discharge of water ought to be deduced, 
and the velocity of the effluent water as due to the whole height of 
water in the reservoir; and by this means his theory became more 
conformable to the results of experience, though still open to 
serious objections. Newton was also the first to investigate the 
difficult subject of the motion of waves (q.v.). 

In 1738 Daniel Bernoulli (1700-1782) published his Hydrodynamica 
seu de viribus et motibus fluidorum commentarii. His theory of 
the motion of fluids, the germ of which was first published in his 
memoir entitled Theoria nova de motu aquarum per canales quocun- 
que fluentes, communicated to the Academy of St Petersburg as 
early as 1726, was founded on two suppositions, which appeared to 
him conformable to experience. He supposed that the surface of 
the fluid, contained in a vessel which is emptying itself by an orifice, 
remains always horizontal; and, if the fluid mass is conceived to be 
divided into an infinite number of horizontal strata of the same 
bulk, that these strata remain contiguous to each other, and that 
all their points descend vertically, with velocities inversely pro- 
portional to their breadth, or to the horizontal sections of the 
reservoir. In order to determine the motion of each stratum, he 
employed the principle of the conservatio virium vivarum, and 
obtained very elegant solutions. But in the absence of a general 
demonstration of that principle, his results did not command the 
• confidence which they would otherwise have deserved, and it 
became desirable to have a theory more certain, and depending solely 
on the fundamental laws of mechanics. Colin Maclaurin (1698- 
1746) and John Bernoulli (1667-1748), who were of this opinion^ 
resolved the problem by more direct methods, the one in his Fluxions, 
published in 1 742, and the other in his Hydraulica nunc primum 
detecta, et demonstrata direcle ex fundamentis pure mechanicis, which 
forms the fourth volume of his works. The method employed by 
Maclaurin has been thought not sufficiently rigorous; and that of 
John Bernoulli is, in the opinion of Lagrange, defective in clearness 
and precision. The theory of Daniel Bernoulli was opposed also by 
Jean le Rond d'Alembert. When generalizing the theory of pendu- 
lums of Jacob Bernoulli (1654-1705) he discovered a principle of 
dynamics so simple and general that it reduced the laws of the 
motions of bodies to that of their equilibrium. He applied this 



n6 



HYDROMECHANICS 



[HYDROSTATICS 



principle to the motion of fluids, and gave a specimen of its applica- 
tion at the end of his Dynamics in 1743. It was more fully developed 
in his Traite des fluides, published in 1744, in which he gave simple 
and elegant solutions of problems relating to the equilibrium and 
motion of fluids. He made use of the same suppositions as Daniel 
Bernoulli, though his calculus was established in a very different 
manner. He considered, at every instant, the actual motion of a 
stratum as composed of a motion which it had in the preceding 
instant and of a motion which it had lost; and the laws of equili- 
brium between the motions lost furnished him with equations re- 
presenting the motion of the fluid. It remained a desideratum to 
express by equations the motion of a particle of the fluid in any 
assigned direction. These equations were found by d'Alembert from 
two principles — that a rectangular canal, taken in a mass of fluid in 
equilibrium, is itself in equilibrium, and that a portion of the fluid, 
in passing from one place to another, preserves the same volume 
when the fluid is incompressible, or dilates itself according to a 
given law when the fluid is elastic. His ingenious method, published 
in 1752, in his Essai sur la resistance des fluides, was brought to per- 
fection in his Opuscules mathematiques , and was adopted by Leonhard 
Euler. 

The resolution of the questions concerning the motion of fluids 
was effected by means of Euler's partial differential coefficients. 
This calculus was first applied to the motion of water by d'Alembert, 
md enabled both him and Euler to represent the theory of fluids 
in formulae restricted by no particular hypothesis. 

One of the most successful labourers in the science of hydro- 
dynamics at this period was Pierre Louis Georges Dubuat (1734- 
1809). Following in the steps of the Abb6 Charles Bossut (Nouvelles 
Experiences sur la resistance des fluides, 1777), he published, in 1786, 
a revised edition of his Principes d'hydraulique, which contains a 
satisfactory theory of the motion of fluids, founded solely upon 
experiments. Dubuat considered that if water were a perfect 
fluid, and the channels in which it flowed infinitely smooth, its 
motion would be continually accelerated, like that of bodies descend- 
ing in an inclined plane. But as the motion of rivers is not continually 
accelerated, and soon arrives at a state of uniformity, it is evident that 
the viscosity of the water, and the friction of the channel in which 
it descends, must equal the accelerating force. Dubuat, therefore, 
assumed it as a proposition of fundamental importance that, when 
water flows in any channel or bed, the accelerating force which obliges 
it to move is equal to the sum of all the resistances which it meets 
with, whether they arise from its own viscosity or from the friction 
of its bed. This principle was employed by him in the first edition 
of his work, which appeared in 1779. The theory contained in that 
edition was founded on the experiments of others, but he soon saw 
that a theory so new, and leading to results so different from the 
ordinary theory, should be founded on new experiments more direct 
than the former, and he was employed in the performance of these 
from 1780 to 1783. The experiments of Bossut were made only on 
pipes of a moderate declivity, but Dubuat used declivities of every 
kind, and made his experiments upon channels of various sizes. 

The theory of running water was greatly advanced by the re- 
searches of Gaspard Riche de Prony (t 755-1839). From a collection 
of the best experiments by previous workers he selected eighty-two 
(fifty-one on the velocity of water in conduit pipes, and thirty-one 
on its velocity in open canals) ; and, discussing these on physical 
and mechanical principles, he succeeded in drawing up general 
formulae, which afforded a simple expression for the velocity of 
running water. 

J. A. Eytelwein (1764-1848) of Berlin, who published in 1801 a 
valuable compendium of hydraulics entitled Handbuch der Mechanik 
und der Hydraulik, investigated the subject of the discharge of water 
by compound pipes, the motions of jets and their impulses against 
plane and oblique surfaces; and he showed theoretically that a water- 
wheel will have its maximum effect when its circumference moves 
with half the velocity of the stream. 

J. N. P. Hachette (1769-1834) in 1816-1817 published memoirs 
containing the results of experiments on the spouting of fluids and the 
discharge of vessels. His object was to measure the contracted part 
of a fluid vein, to examine the phenomena attendant on additional 
tubes, and to investigate the form of the fluid vein and the results 
obtained when different forms of orifices are employed. Extensive 
experiments on the discharge of water from orifices (Experiences 
hydrauliques, Paris, 1832) were conducted under the direction of the 
French government by J. V. Poncelet (1788-1867) and J. A. Lesbros 
(1790-1860). P. P. Boileau (1811-1891) discussed their results and 
added experiments of his own [Traite de la tnesure des eaux courantes, 
Paris, 1854). K. R. Bornemann re-examined all these results with 
great care, and gave formulae expressing the variation of the co- 
efficients of discharge in different conditions (Civil lngtnieur, 1880). 
Julius Weisbach (1806-1 871) also made many experimental in- 
vestigations on the discharge of fluids. The experiments of J. B. 
Francis (Lowell Hydraulic Experiments, Boston, Mass., 1855) led him 
to propose variations in the accepted formulae for the discharge over 
weirs, and a generation later a very complete investigation of this 
subject was carried out by H. Bazin. An elaborate inquiry on the 
flow of water in pipes and channels was conducted by H. G. P. 
Darcy (1803-1858) and continued by H. Bazin, at the expense of the 
French government (Recherches hydrauliques, Paris, 1866). German 



engineers have also devoted special attention to the measurement 
of the flow in rivers; the Beitrdge zur Hydrographie des Konig- 
reiches Bbhmen (Prague, 1872-1875) of A. R. Harlacher (1842-1890) 
contained valuable measurements of this kind, together with a com- 
parison of the experimental results with the formulae of flow that had 
been proposed up to the date of its publication, and important data 
were yielded by the gaugings of the Mississippi made for the United 
States government by A. A. Humphreys and H. L. Abbot, by Robert 
Gordon's gaugings of the Irrawaddy, and by Allen J. C. Cunningham's 
experiments on the Ganges canal. The friction of water, investigated 
for slow speeds by Coulomb, was measured for higher speeds by 
William Froude (1810-1879), whose work is of great value in the 
theory of ship resistance (Brit. Assoc. Report., 1869), and stream line 
motion was studied by Professor Osborne Reynolds and by Professor 
H. S. Hele Shaw. (X.) 

Hydrostatics 
Hydrostatics is a science which grew originally out of a number 
of isolated practical problems; but it satisfies the requirement 
of perfect accuracy in its application to phenomena, the largest 
and smallest, of the behaviour of a fluid. At the same time, 
it delights the pure theorist by the simplicity of the logic with 
which the fundamental theorems may be established, and by the 
elegance of its mathematical operations, insomuch that hydro- 
statics may be considered as the Euclidean pure geometry of 
mechanical science. 

1 . The Different Slates of a Substance or Matter. — All substance 
in nature falls into one of the two classes, solid and fluid; a 
solid substance, the land, for instance, as contrasted with a 
fluid, like water, being a substance which does not flow of itself. 

A fluid, as the name implies, is a substance which flows, or 
is capable of flowing; water and air are the two fluids distributed 
most universally over the surface of the earth. 

Fluids again are divided into two classes, termed a liquid 
and a gas, of which water and air are the chief examples. 

A liquid is a fluid which is incompressible or practically so, 
i.e. it does not change in volume sensibly with change of pressure. 

A gas is a compressible fluid, and the change in volume is 
considerable with moderate variation of pressure. 

Liquids, again, can be poured from one open vessel into another, 
and can be kept in an uncovered vessel, but a gas tends to diffuse 
itself indefinitely and must be preserved in a closed reservoir. 

The distinguishing characteristics of the three kinds of sub- 
stance or states of matter, the solid, liquid and gas, are summarized 
thus in 0. Lodge's Mechanics: — 

A solid has both size and shape. 
A liquid has size but not shape. 
A 1 gas has neither size nor shape. 

2. The Change of State of Matter. — By a change of temperature 
and pressure combined, a substance can in general be made to 
pass from one state into another; thus by gradually increasing 
the temperature a solid piece of ice can be melted into the liquid 
state of water, and the water again can be boiled off into the 
gaseous state as steam. Again, by raising the temperature, 
a metal in the solid state can be melted and liquefied, and poured 
into a mould to assume any form desired, which is retained when 
the metal cools and solidifies again; the gaseous state of a metal 
is revealed by the spectroscope. Conversely, a combination 
of increased pressure and lowering of temperature will, if carried 
far enough, reduce a gas to a liquid, and afterwards to the solid 
state; and nearly every gaseous substance has now undergone 
this operation. 

A certain critical temperature is observed in a gas, above which 
the liquefaction is impossible; so that the gaseous state has two 
subdivisions into (i.)a true gas, which cannot be liquefied, because 
its temperature is above the critical temperature, (ii.) a vapour, 
where the temperature is below the critical, and which can 
ultimately be liquefied by further lowering of temperature or 
increase of pressure. 

3. Plasticity and Viscosity. — Every solid substance is found to 
be plastic more or less, as exemplified by punching, shearing 
and cutting; but the plastic solid is distinguished from the 
viscous fluid in that a plastic solid requires a certain magnitude 
of stress to be exceeded to make it flow, whereas the viscous 
liquid will yield to the slightest stress, but requires a certain 
length of time for the effect to be appreciable. 



HYDROSTATICS] 



HYDROMECHANICS 



117 



According to Maxwell (Theory of Heat) " When a continuous 
alteration of form is produced only by a stress exceeding a certain 
value, the substance is called a solid, however soft and plastic 
it may be. But when the smallest stress, if only continued long 
enough, will cause a perceptible and increasing change of form, 
the substance must be regarded as a viscous fluid, however hard 
it may be." Maxwell illustrates the difference between a soft 
solid and a hard liquid by a jelly and a block of pitch; also by 
the experiment of supporting a candle and a stick of sealing- 
wax; after a considerable time the sealing-wax will be found 
bent and so is a fluid, but the candle remains straight as a solid. 

4. Definition of a Fluid. — A fluid is a substance which yields 
continually to the slightest tangential stress in its interior; 
that is, it can be divided very easily along any plane (given plenty 
of time if the fluid is viscous) . It follows that when the fluid has 
come to rest, the tangential stress in any plane in its interior 
must vanish, and the stress must be entirely normal to the plane. 
This mechanical axiom of the normality oj fluid pressure is the 
foundation of the mathematical theory of hydrostatics. 

The theorems of hydrostatics are thus true for all stationary 
fluids, however, viscous they may be; it is only when we come 
to hydrodynamics, the science of the motion of a fluid, that 
viscosity will make itself felt and modify the theory; unless we 
begin by postulating the perfect fluid, devoid of viscosity, so 
that the principle of the normality of fluid pressure is taken to 
hold when the fluid is in movement. 

5. The Measurement of Fluid Pressure. — The pressure at any point 
of a plane in the interior of a fluid is the intensity of the normal 
thrust estimated per unit area of the plane. 

Thus, if a thrust of P lb is distributed uniformly over a plane 
area of A sq. ft., as on the horizontal bottom of the sea or any 
reservoir, the pressure at any point of the plane is P/A lb per sq. ft., 
or P/144A lb per sq. in. (lb/ft. 2 and lb/in. 2 , in the Hospitalier notation, 
to be employed in the sequel). If the distribution of the thrust is 
not uniform, as, for instance, on a vertical or inclined face or wall of a 
reservoir, then P/A represents the average pressure over the area ; and 
the actual pressure at any point is the average pressure over a small 
area enclosing the point. Thus, if a thrust AP lb acts on a small plane 
area AA ft. 2 enclosing a point B, the pressure p at B is the limit of 
AP/AA ; and 

/>=lt(AP/AA)=<iP/(iA, (1) 

in the notation of the differential calculus. 

6. The Equality of Fluid Pressure in all Directions. — This funda- 
mental principle of hydrostatics follows at once from the principle of 
the normality of fluid pressure implied in the definition of a fluid in 
§ 4. Take any two arbitrary directions in the plane of the paper, and 
draw a small isosceles triangle abc, whose sides are perpendicular 
to the two directions, and consider the equilibrium of a small triangular 
prism of fluid, of which the triangle is the cross section. Let P, Q 
denote the normal thrust across the sides be, ca, and R the normal 
thrust across the base ab. Then, since these three forces main- 
tain equilibrium, and R makes equal angles with P and Q, therefore 
P and Q must be equal. But the faces be, ca, over which P and Q 
act, are also equal, so that the pressure on each face is equal. A 

scalene triangle abc might also be employed, or a 
tetrahedron. 

It follows that the pressure of a fluid requires 
to be calculated in one direction only, chosen as 
the simplest direction for convenience. 

7. The Transmissibility of Fluid Pressure. — Any 
_ _ additional pressure applied to the fluid will be 

2 - — = — transmitted equally to every point in the case of 
J2-EZE-. a liquid; this principle of the transmissibility of 
pressure was enunciated by Pascal, 1653, and 
applied by him to the invention of the hydraulic 
press. 
This machine consists essentially of two communicating cylinders 
(fig. la), filled with liquid and closed by pistons. If a thrust P lb is 
applied to one piston of area A ft. s , it will be balanced by a thrust 
W lb applied to the other piston of area B ft. 8 , where 



I 




level, and considering the equilibrium of a thin prism of liquid AB, 
bounded by planes at A and B perpendicular to AB. As gravity 
and the fluid pressure on the sides of the prism act at right angles 
to AB, the equilibrium requires the equality of thrust on the ends 
A and B ; and as the areas are equal, the pressure must be equal at 
A and B ; and so the pressure is the same at all points in the same 
horizontal plane. If the fluid is a liquid, it -■ ■-, 
can have a free surface without diffusing 
itself, as a gas would; and this free surface, 
being a surface of zero pressure, or more 
generally of uniform atmospheric pressure, 
will also be a surface of equal pressure, and 
therefore a horizontal plane. 

Hence the theorem. — The free surface of 
a liquid at rest under gravity is a horizontal 
plane. This is the characteristic distinguish- 
ing between a solid and a liquid; as, for in- 
stance, between land and water. The land 
has hills and valleys, but the surface of 
water at rest is a horizontal plane; and if 
disturbed the surface moves in waves. 

9. Theorem. — In a homogeneous liquid at 
rest under gravity the pressure increases 
uniformly with the depth. 

This is proved by taking the two points 
A and B in the same vertical line, and 
considering the equilibrium of the prism by 
resolving vertically. In this case the thrust 
at the lower end B must exceed the thrust 
at A, the upper end, by the weight of the 
prism of liquid; so that, denoting the cross 
section of the prism by a ft. 2 , the pressure at A and By by pa and 
p lb/ft. 2 , and by w the density of the liquid estimated in lb/ft. 3 , 



Fig. 10. 



/> = P/A = W/B, 



(1) 



the pressure p of the liquid being supposed uniform; and, by 
making the ratio B/A sufficiently large, the mechanical advantage 
can be increased to any desired amount, and in the simplest manner 
possible, without the intervention of levers and machinery. 

Fig. lb shows also a modern form of the hydraulic press, applied 
to the operation of covering an electric'cable with a lead coating. 

8. Theorem. — In a fluid at rest under gravity the pressure is the 
same at any two points in the same horizontal plane; in other 
words, a surface of equal pressure is a horizontal plane. 

This is proved by taking any two points A and B at the same 




pa— poa—wa. AB, 
p=a.kB+p . 



(I) 
(2) 



Thus in water, where w = 62-4lb/ft. s , the pressure increases 
62-4 lb/ft. 1 , or 62-44- 144 =0-433 lb/in. 2 for every additional foot of 
depth. 

10. Theorem. — If two liquids of different density are resting in 
vessels in communication, the height of the free surface of such liquid 
above the surface of separation is inversely as the density. 

For if the liquid of density a rises to the height h and of density p 
to the height fe^and po denotes the atmospheric pressure, the pressure 
in the liquid at the level of the surface of separation will be ah+pt 
and pk+po, and these being equal we have 



oh=pk. 



(1) 



The principle is illustrated in the article Barometer, where a 
column of mercury of density a and height h, rising in the tube to the 
Torricellian vacuum, is balanced by a column of air of density p, 
which may be supposed to rise as a homogeneous fluid to a height k, 
called the height of the homogeneous atmosphere. Thus water Deing 
about 800 times denser than air and mercury 13-6 times denser 
than water, 

£/fc = (r/p = 8ooXi3-6 = io,88o; (2) 

and with an average barometer height of 30 in. this makes k 27,200 
ft., about 8300 metres. 

1 1 . The Head of Water or a Liquid. — The pressure ah at a depth 
h ft. in liquid of density a is called the pressure due to a head of h ft. 
of the liquid. The atmospheric pressure is thus due to an average 
head of 30 in. of mercury, or 30X13-6-7-12 =34 ft. of water, or 
27,200 ft. of air. The pressure of the air is a convenient unit to 
employ in practical work, where it is called an " atmosphere "; it is 
made the equivalent of a pressure of one kg/cm 2 ; and one ton/inch 2 , 
employed as the unit with high pressure as in artillery, may be taken 
as 150 atmospheres. 

12. Theorem. — A body immersed in a fluid is buoyed up by a force 
equal to the weight of the liquid displaced, acting vertically upward 
through the centre of gravity of the displaced liquid. 

For if the body is removed, and replaced by the fluid as at first, 
this fluid is in equilibrium under its own weight and the thrust of the 
surrounding fluid, which must be equal and opposite, and the sur- 
rounding fluid acts in the same manner when the body replaces the 
displaced fluid again; so that the resultant thrust of the fluid a"cts 
vertically upward through the centre of gravity of the fluid displaced,- 
and is equal to the weight. 

When the body is floating freely like a ship, the equilibrium of 
this liquid thrust with the weight of the ship requires that the weight 
of water displaced is equal to the weight of the ship and the two 
centres of gravity are in the same vertical line. So also a balloon 
begins to rise when the weight of air displaced is greater than the 
weight of the balloon, and it is in equilibrium when the weights are 
equal. This theorem is called generally the principle of Archimedes. 

It is used to determine the density of a body experimentally; 
for if W is the weight of a body weighed in a balance in air (strictly 
in vacuo), and if W' is the weight required to balance when the 
body is suspended in water, then the upward thrust of the liquid 



U8 



HTOROMEGHANICS 



[HYE>R6STATICS 




or weight of liquid displaced is W-W, so that the specific gravity 
(S.G.) r i defined 1 as the ratio of the weight of a body to the weight 
of an equal volume of water 1 , is W/(W-W). 

As stated first by Archimedes, the principle asserts the obvious 
fact that a body displaces its own vorume of water; and he utilized it 
in the problem of the determination of the adulteration of the crown 
of Hiero. He weighed out a lump of gold and of silver of the same 
weight *s the clown; and, immersing the three in succession in 
water, he found they spilt over measures of water in the ratio 
t 1 ? -A;i& or 33: 24: 44; thence it follows that the gold : silver alloy 
of tfiefiorown was as 1 1 : 9 by weight. 

13. Theorem. — The resultant vertical thrust on any portion of a 
curyed suffice exposed to the pressure of a fluid at rest under 
gravity is the weifrht of fluid cut out by vertical lines drawn round 
the .boundary of the curved surface. 

TTieorent.—^-The resultant horizontal thrust in any direction is 
obtilned by\ dr$t\fShg parallel horizontal lines round the boundary, 
and- intejfsecting i plane perpendicular to their direction in a plane 
curve; and then investigating the thrust on this plane area, which 
will, be tfce same as on the curved surface. 

The iSe&of of these theorems proceeds as before, employing the 
normality principle; they are required, for instance, in the deter- 
minatidn of the liquid thrust on any portion of the bottom of a ship. 
In casting a thin hollow object like a bell, it will be seen that the 
resultant upward thrust on the mould may be many times greater 
than the weight of metal; many a curious' experiment has been 
devised to illustrate this property and classed 3s a hydrostatic 
paradox (Boyle,' Hydrostatical Paradoxes, 1666). 

Consider,, for instance, the operation of casting a hemispherical 
bell, in fig. 2. As the molten metal is run in, the upward thrust on- 

the outside mould, when 

K' *i •" - - ■ K j the level has Teached 

PP', is the weight of 
metal in the volume gen- 
erated by the revolution 
of APQ; and this, by a 
theorem of, Archimedes, 
has the same volume as 
the cone ORR', or iir^*, 
where y is the depth of 
metal, the horizontal 
sections being equal so 
long as y is less than the 
radius of the outside 
hemisphere. Af terwai 'd s » 
, when the metal has risen 

above B, to the level KK', the additional thrust is the weight of 
the cylinder of diameter KK' and height BH. The upward thrust 
is the same, however thin the metal may be in the interspace 
between the outer mould and the core inside; and this was formerly 
considered paradoxical. 

A nalytical Equations of Equilibrium of a Fluid at rest under any 
System of Force. ■..'.', 

14. Referred to three fixed coordinate axes, a fluid, in which 
the pressure is p, the density p, and X, Y, Z the components of 
impressed force per unit mass, requires for the equilibrium of the part 
filling a fixed surface S, on resolving parallel to Ox, 

JJlpdS =jjfp^dxdydz, 

where I, m, n denote the direction cosines of the normal 
outward of the surface Si • 

But by Green's transformation 

fJlpdS=Jff d £dxdydz, 
thus leading to the differential relation at every point 

The three equations of equilibrium obtained by taking moments 
round the axes are then found to be satisfied identically. 

Hence the space variation of the pressure in any direction, or the 
pressure-gradient, is the resolved force per unit volume in that 
direction. : The resultant force is therefore in the direction of the 
steepest pressure-gradient, and this is normal to the surface of equal 
pressure; for equilibrium to exist in a fluid the lines of force must 
therefore be capable of being cut orthogonally by a system of 
surfaces, which will be surfaces of equal pressure. 

Ignoring temperature effect, and taking the density as a function 
of the pressure, surfaces of equal pressure are also of equal density, 
and the fluid is stratified by surfaces orthogonal to the lines of force; 

\%-\%'\%^>l "■■;. (4) 

are the partial differential coefficients of some function ¥,=*fdplp, 
of *, y, z; so that X, Y, Z must be the partial differential coefficients 
of * potential -V, such that the force in any direction is the down- 
ward gradient of V ; and then 

./ i . ZF+ar*" ' orP,+V=»constant, (S) 



Fig. 2. 



= pZ. 



(1) 
drawn 



(2) 



(3) 



in which P may be 'called the hydrostatic head and V the head of 
potential. • 

With variation of temperature, the surfaces of equal pressure and 
density need not coincide; but, taking the pressure, density and 
temperature as connected by some relation^ such as the gas-equation, 
the surfaces of equal density and temperature must intersect in lines 
lying on a surface of equal pressure. 

15. As an. .example, of the general equations, take the simplest 
case of a uniform field of gravity, with Oz directed vertically down- 
ward ; employing the gravitation unit of force, 



I dp_ 1 dp _ 1 dp 
pdx~°' P~d~y" > ~J*~ 1 ' 



(1) 



P ay • p dz 
P=J<i^/p=z-f-a constant. (2) 

When the density p is uniform, this becomes, as before in (2) § 9 

p=pz+p«. (3) 

Suppose the density p varies as some nth power of the depth 
below 0, then 

dp/dz-p — ptz" (4) 



P-IK 



'n + l W 



(5) 



££_. 
n + l n + l~ 
supposing p and p to vanish together. 

These equations can be' made to represent the state of convective 
equilibrium of the atmosphere, depending on the gas-equation 

/> = p£ = Rp0, (6) 

where denotes the absolute temperature ; and then 



r,d»_d (p\ i_ 

<fe 3zW~»+i' 



(7) 



so that the temperature-gradient dd/dz is constant, as in convective 
equilibrium in (11). 

From the gas-equation, in general, in the atmosphere 

1 dp_i,d£^_i d$_p__i <Z0_i_i d$ .. 

pdz~p dz~B dz~p 6<Iz~% 6 dz' ^ ' 

which is positive, and the density p diminishes with the ascent, 
provided the temperature-gradient de/dz does not exceed 9/k. 

With uniform temperature, taking h constant in the gas-equation, 
dpfdz=-p~p/k, p = poe' lh ,, (9) 

so that in ascending in the atmosphere of thermal equilibrium the 
pressure and density diminish at compound discount, and for 
pressures pi arid pi at heights zi arid z 2 

(zi-Z2)/*=log,(£ 2 /£i)=2.3logio(/>2/£i). (10) 

In the convective equilibrium of the atmosphere, the air is sup- 
posed to change in density and pressure without exchange of heat by 
conduction ; and then 

p/po = (9/eo) n , ^o = (9/9o)» +1 , (II) 

dz \ dp . ,. .* , . ._ ,1 

d8 = p-m = ( n+I) pi=( n + I)R ' 7=I +»- 

where y is the ratio of the specific heat at constant pressure and 
constant volume. 

In the mqre gerteral case of the convective equilibrium of a spherical 
atmosphere surrounding the earth, of radius a, 



P, ■(•■+»>S5— r**' 



(12) 



gravity varying inversely as the square of the distance r from the 
centre; so that, A=*po/.pa, denoting the height of the homogeneous 
atmosphere at the surface,:^ is given by 

(«+i>ft(i-tf/9o)=o(i-o/r), (13). 

or if c denotes the distance where 9 = o, 



(14); 



0o~r ' c — a' 

When the compressibility of water is taken into account in: a 
deep ocean, an experimental law must be employed, such as ! • 

p— p„ = k(j>— po), or pfp -i + (p— po)!K X = *po, .(15) 
so that X is the pressure due to a head k of the liquid' at density po 
under atmospheric pressure po\ and it is the gauge pressure required 
on this law to double the density. Then 

dp/dz = kdpldz** P , p = poe*'*, p-po = kpt,(.e'"'-i); (16) 
and if the liquid Was incompressible, the depth at pressure p would 
be (p—po)/po, so that the lowering of the surface due tocompressionTs 

ke'l k — k—z = %z?lk, when k is large. (17) 

For sea water, X is about 25,000 atmospheres, and k is then 25,000 
times the height of the water barometer, about 250,000 metres, so 
that in an ocean 10 kilometres deep the level is lowered about 200 
metres by the compressibility of the water; and the density at the 
bottom is increased 4 %. 

On another physical assumption of constant cubical elasticity A. 
&p*>\dplp, (/>'~fc»)/X=log(p/po), (18) 

z3 "/t ai = * p ' \pt pi ' p k' 



\**kpt, (19) 



HYPfcOSXATie?} 



r. 



HlCDRQAifEGHftNIGS 



■J 19 



and the lowering of the surface is 



^~2 = Alog^-z«-Mog(i-!) r-.zft;^ (20) 



(3) 
(4) 
(5) 



: (6) 
(7) 
(8) 
(9) : 



Po °ft " ""°\" ft/ '"""'*B 

as before in 17). 

16. Centre of Pressure. — A plane area exposed to fluid pressure 
on one side experiences a, single resultant thrust, the integrated 
pressure over the area, acting through a definite point called 
the centre of pressure (C.P.) of the area. 
Thus if the plane is normal to Ox, the resultant.thrust 

R^jfpdxdy, . .. , ' (1). 

and the co-ordinates x, y of the C.P. are given by 

xR=ffxpdXdy, yR= ffypdxdy. - (2) 

The C.P. is thus the C.G. of a plane lamina bounded by the area, 
in which the surface density is p. 

If p is uniform, the C.P. and C.G. of the area coincide. 
For a homogeneous liquid at rest under gravity, p is proportional . 
to the depth below the surface, i.e. to the perpendicular distance 
from the line of intersection of the plane of the area with the free 
surface of the liquid. 

If the equation of this line, referred to new coordinate axes in the 
plane area, is written 

x cos a -+• y sin a — h — O, 

R = ffp(h—xcos a— y sin a)dxdy, 

iR= fjpx(h-+x cos o— ysin w)dxdy, 

yR=fjpy(h — xcosa — y sin a)dxdy. 

Placing the new origin at the C.G. of the area A, 

ffxdxdy=o, fjydxdy^o, 

R = P«A,; 

xhA = —cos affx 2 dA— sin affxydA, 
yh A = — cos affxydA — sin a ffy*dA . 
Turning the axes to make them coincide with the pr'yiqipal axes 
of the area A, thus making JfxydA = o, \ 

xh= — a'coso, yft = — ft'sinoi (to) 

where 

f(x*dA^Aa*. //y'dA=A6', . (n) 

a and b denoting the semi-axes of the momental ellipse of the area. 

This shows that the C.P. is the antipole ofthejineof intersection of 
its plane with the free surface with respect to the momehtal ellipse at 
the C.G. of the area. 

Thus the C.P. of a rectangle or parallelogram with a side in the 
surface is at § of the depth of the tower side; of a triangle with a 
vertex in the surface and base horizontal is J of the depth of the base ; 
but if the base is in the surface, the C.P. is at half the depth of the 
vertex; as on the faces of a tetrahedron', with one edge in the 
surface. 

The core of an area is the name giver) tp the limited area round 
its C.G. within which the C.P. must He when the area is immersed 
completely; the boundary of the core is therefore the locus of the 
antipodes with respect to the momental ellipse of water lines which 
touch the boundary of_ the area. Thus the core of a circle or an 
ellipse is a concentric circle or ellipse of one quarter the size ; 

The C.P. of water lines passing through a fixed point lies ona 
straight line, the antipolar of the point; and thus the core of a tri- 
angle is a similar triangle of one quarter the size, and the core of a 
parallelogram is another parallelogram, the diagonals of which are 
the middle third of the median lines. 

In the design of a structure such as a tall reservoir dam it is 
important that the line of thrUst in the material should pass inside 
the core of a section, so that' the material should not be in a state 
of tension anywhere and so liable to open and admit the water. 

17. Equilibrium and Stability of a Ship or Floating Body. 
The Metacenlre.—-The principle of Archimedes, in § 12 leads 

immediately . to the 
conditions of equili- 
brium of a body sup- 
ported freely in fluid, 
like a fish in water or 
a balloon in the air, 
or like a ship (fig, 3) 
floating partly im- 
mersed in water and 
the rest in air. The 
body is in equili- 
brium under two 
forces: — (i.) its 
weight W acting 
vertically . downward 
through G, the C.G. of the body, and (ii.) the buoyancy of the 
fluid, equal to the weight of the displaced fluid, and acting 
vertically upward through B, the C.G. of the displaced fluid; 







I""' 


r* 








M 








L 




G 

F 


iGt 






2* 


V 




B, 


J 


s±~r 



for equilibriufii these two forces must be equal and opposite in 
the same line. 

The conditions of equilibrium of a body, floating like a ship 
on the surface of a liquid, are therefore: — 

(i.) the weight of the body must be less than the weight of the 
total volume of liquid it can displace; or else the body will sink 
to the bottom of the liquid; the difference of the weights is 
called the "reserve of buoyancy." 

(ii.) the weight of liquid which the body displaces in the 
position of equilibrium is equal to. the weight W of the body; and 

(iii.) the C.G.j B, of the liquid displaced and G of the body, 
must lie in the same vertical line GB. 

18. In addition to . satisfying these conditions of equilibrium, 
a ship must fulfil the further condition of stability, so as to keep 
upright; if displaced slightly from this position, the forces 
called into play must be such as to restore the ship to the upright 
again. The stability of a ship, is investigated practically by 
inclining it; a weight is moved across the deck and the angle is 
observed of the heel produced. 

Suppose P tons is moved c ft. across the deck of a ship of W tons 
displacement! the C.G. Will move from G to Gi the reduced distance 
GiCa = c (P/W); and if B, called the centre of buoyancy, moves 
to Bi, along the curye of buoyancy BBi, the normal of this curve at 
Bi will be the new vertical B.1G1, meeting the old vertical in a point 
Kl, the centre of curvature of BBi, called the metacentre. 
• If the ' ship heels J through an angle or a slope of r in m, 

GM = GGic6t9=mc(P/W), (1) 

and GM is called the metacentric height; and the ship must be 
Joallasted, so that G lies below M. If G was above M, the tangent 
drawn from G to the evolute of B, and normal to the curve of buoyancy, 
would: give the vertical, in a new position of equilibrium. Thus in 
H.M.S. "Achilles" of. 9000 tons displacement it was found that 
moving 20 tons' across the deck, a distance of 42 ft., caused the bob 
of a pendulum 20! ft. long to move through ro in., so that ' 



K 

Fig. 3. 



GM, 



24°\>.„\. 20 r 

= -iF* 42X 9 -5oo^ 2 ' 2 4 f t.;. 



..(*> 



also 

potfl-24, 0=2° 24'. (3),. 

In.a diagram it is_CQnducive.to clearness to draw the ship in on* 
position, and to incline the water-line; and the p^ge can be turned 
if it is desired to bring the new water-line horizontal. 

Suppose the ship turns about an axis through F in the water-line 
area, perpendicular to the plane of the paper; denoting by y the 
distance of an element dA if the water-line area from the axis of 
rotation; the change of displacement is XydA tan 0, so that there is 
ho change of displacement if 2ydA=o, that is, if the qxi^ passes 
through the C.G. of the water-line area, which we denote by F 
and call the centre of flotation. 

The righting couple of the wedges of immersion and emersion 
will be 

XwydA tiin&.y = w tan 6ifdA = w tan 0.A& 2 ft. tons, (4) 

■w denoting the density of water in tons/ft. 3 , and W=k»V, for a 
displacement of V ft. 3 

This couple, combined with the original buoyancy W through B, 
is equivalent to the new buoyancy through B, so that 

W.BBj^wA^tanfl, (5) 

• BM=BB 1 cot0 = A^/V, (6) 

giving the radius of curvature BM of the curve of buoyancy B, in 
terms of the displacement V, and Ak 2 the moment of inertia of the 
water-line area about /an axis through F, perpendicular to the- plane 
of displacement, , . 

An inclining couple due to moving a weight about in a ship will heel 
the, ship about an axis perpendicular to the plane of the couple* only 
when this axis is a principal axis at F of the momental ellipse of 
the water-line area A. For if the ship turns through a small angle; 
about the line FF.', then bi, 62, the C.G. qf the wedge of imwerslion 
and emersion, w)ll be the C.P. with respect to FF' of the two parts of 
the water-line area, so that JA will be conjugate to FF' with respect 
to the momental ellipse at F. . ' * ; 

The naval architect distinguishes between the stability of, form, 
represented by the righting couple W.BM, and the stability ' oj ' baUast- 
ing, represented by W.BG. Ballasted with G at B, the righting 
couple when the ship is heeled through 0is given by W.BM. tan0; but 
if weights inside the ship are raised to bring G above B, the righting 
couple is diminished. b_y, W.BG. tan 0, so that the resultant righting 
couple is W,GM/ tan '0. Provided the ship is designed to 'float 
upright at the smallest draft with no load on board, the stability 
at any other draft of water can be arranged by the stowage of the 
weight, high or low. 

19. Proceeding as in § 16 for the determination of the C.P. of an 
area, the same argument will show that an inclining couple due to 



120 



HYDROMECHANICS 



(HYDRODYNAMICS 



the movement of a weight P through a distance c will cause the ship 
to heel through an angle about an axis FF' through F, which is 
conjugate to the direction of the movement of P with respect to an 
ellipse, not the mdmental ellipse of the water-line area A, but a 
confocal to it, of squared semi-axes 

a J -W/A, P-AV/A, (i) 

h denoting the vertical height BG between C.G. and centre of 
buoyancy. The varying direction of the inclining couple Pc may be 
realized by swinging the weight P from a crane on the ship, in a circle of 
radius c. But if the weight P was lowered on the ship from a crane 
on shore, the vessel would sink bodily a distance P/wA if P was 
deposited over F; but deposited anywhere else, say over Q on the 
water-line area, the ship would turn about a line the antipolar of Q 
with respect to the confocal ellipse, parallel to FF', at a distance FK 
from F 

FK = (#-W/A)/FQsinQFF' (2) 

through an angle $ or a slope of one in m, given by 

sin9= ^=i?A^ = W-ApIV F Q sin 2 FF '' ( 3> 

where k denotes the radius of gyration about FF' of the water-line 
area. Burning the coal on a voyage has the reverse effect on a 
steamer. 

Hydrodynamics 
20. In considering the motion of a fluid we shall suppose it 
non-viscous, so that whatever the state of motion the stress 
across any section is normal, and the principle of the normality 
and thence of the equality of fluid pressure can be employed, as 
in hydrostatics. The practical problems of fluid motion, which 
are amenable to mathematical analysis when viscosity is taken 
into account, are excluded from treatment here, as constituting 
a separate branch called "hydraulics" (q.v.). Two methods are 
employed in hydrodynamics, called the Eulerian and Lagrangian, 
although both are due originally to Leonhard Euler. In the 
Eulerian method the attention is fixed on a particular point of 
space, and the change is observed there of pressure, density 
and velocity, which takes place during the motion; but in the 
Lagrangian method we follow up a particle of fluid and observe 
how it changes. The first may be called the statistical method; 
and the second the historical, according to J. C. Maxwell. The 
Lagrangian method being employed rarely, we shall confine 
ourselves to the Eulerian treatment. 

The Eulerian Form of the Equations of Motion. 

21. The first equation to be established is the equation of 
continuity, which expresses the fact that the increase of matter 
within a fixed surface is due to the flow of fluid across the surface 
into its interior. 

In a straight uniform current of fluid of density p, flowing with 
velocity q, the flow in units of mass per second across a plane area A, 
placed in the current with the normal of the plane making an angle 8 
with the velocity, is oAq cos 0, the product of the density p, the area 
A, and q cos the component velocity normal to the plane. 

Generally if S denotes any closed surface, fixed in the fluid, M the 
mass of the fluid inside it at any time t, and 9 the angle which the 
outward-drawn normal makes with the velocity q at that point, 

d"Stl/dt =rate of increase of fluid inside the surface, (1) 

= flux across the surface into the interior ■ 
= ~JJpq cos 0<ZS, 
the integral equation of continuity. 

In the Eulerian notation u, v, w denote the components of the 
velocity q parallel to the coordinate axes at any point (x, y, z) at the 
time t; u, v, w are functions of x, y, 2, /, the independent variables; 
and d is used here to denote partial differentiation with respect to 
any one of these four independent variables, all capable of varying 
one at a time. 

To transfer the integral equation into the differential equation of 
continuity, Green's transformation is required again, namely, 

/// CS+S+S) dxdydz =//^+ M "+«f )«, (2) 

or individually 



which becomes by Green's transformation 

leading to the differential equation of continuity when the integration 
is removed. 

22. The equations of motion can be established in a similar 
way by considering the rate of increase of momentum in a fixed 
direction of the fluid inside the surface, and equating it to the 
momentum generated by the force acting throughout the space 
S, and by the pressure acting over the surface S. 

Taking the fixed direction parallel to the axis of x, the time-rate 
of increase of momentum, due to the fluid which crosses the surface, is 



-f fpuq cos 9dS = -ff{lpu i +mpuv+npuiv)dS, (1) 

which by Green's transformation is 

The rate of generation of momentum in the interior of S by the 
component of force; X per unit mass, is 

fffpXdxdydz, (3) 

and by the pressure at the surface S is 

-JJlpdS = -fjj d £lxdydz, (4) 

by Green's transformation. .... 

The time rate of increase of momentum of the fluid inside S is 



w 



' d(pu) 
dt 



■dxdydz ; 



and (5) is the sum of (1), (2), (3), (4), so that 

leading to the differential equation of motion 

dpu , dpu* , dpuv . dpuw _ \r_d]> 
~Sy~ 



dpuw v 



dx' 



(5) 



(6) 



(7) 



with two similar equations. 

The absolute unit of force is employed here, and not the gravitation 
unit of hydrostatics; in a numerical application it is assumed that 
C.G.S. units are intended. 

These equations may be simplified slightly, using the equation of 
continuity (5) §21; for 

dpu 
It' 



dpu* , dpuv , dpuw 
r_ d7 + dy + 



dz 



(du . du . du . du\ 
= p Xdi+ u Tx +v dy- +w Tz) 
j... (dp .dpu dpv dpw\ 
+u \dt + -d-x-+-% + -dT)' 



(8) 



reducing to the first ljne, the second line vanishing in consequence of 
the equation of continuity; and so the equation of motion may be 
written in the more usual form 

du , du , du , du -v idp /„% 

3r+«s+ B 3y +u, ar" x "7S' (9) 

with the two others 



dv 



+«; 



d7 T "3x 



dv , dv . dv v I dp 



dy 
dw 



dz 
dw 



(io) 



ffff/xdydz-ffWS 



(3) 

where the integrations extend throughout the volume and over the 
surface of a closed space S; I, m, n denoting the direction cosines 
of the outward-drawn normal at the surface element <2S, and £, ij, f 
any continuous functions of x, y, 2. 

The integral equation of continuity (1) may now be written 

! z£dxdydz+ff(lpu+mpv+npw)dS=o, (4) 



fffi 



pdy' 
dw , dw , dw , dw 1 1 dp 
H+ u Tx +v dy-+ w dz- =Z -pTz- 

23. As a rule these equations are established immediately 
by determining the component acceleration of the fluid particle 
which is passing through (x, y, z) at the instant t of tiwie con- 
sidered, and saying that the reversed acceleration or kinetic 
reaction, combined with the impressed force per unit of mass 
and pressure-gradient, will according to d'Alembert's principle 
form a system in equilibrium. 

To determine the_ component acceleration of a particle, suppose'E, 
to denote any function of x, y, z, t, and investigate the time rate of F 
for a moving particle ; denoting the change by DF /dt, 



DF = , F(x+uSl, y+vM, z+wSt, t+St)-¥(x, y, 2, t) 
IT it 



dF 



dF . dF . 



(I? 



,-,.", dF, 
~^i+ u dx- +v ly- +w dz-' 

and D/dt is called particle differentiation, because it follows the rate 
of change of a particle as it leaves the point x, y, 2; but 

dF/dt, dF/dx, dF/dy, dF/dz (2) 

represent the rate of change of F at the time t, at the point, *, y, z, 
fixed in space. 



HYDRODYNAMICS] 



HYDROMECHANICS 



121 



The components of acceleration of a particle of fluid are conse- 
quently 



Dm du . du . du . du 



dv 



(3) 
(4) 

(5) 



dt ~ dt ^"di^'dy 
Dr dv , dv , dv , 

-dT=Ji+ u dH +v d^+ w ^ 

Dw dw , dw , dw , dw 

-dT = W+ u -dH +v -dy +w Tz 
leading to the equations of motion above. 

If F (x, y, z, /) =o represents the equation of a surface containing 
always the same particles of fluid, 

DF dF , dF . dF . dF ,,, 

It = °' 0T dt +u di +v ly +W &~ < (6 > 

which is called the differential equation of the bounding surface. 
A bounding surface is such that there is no flow'of fluid across it, 
as expressed by equation (6). The surface always contains the same 
fluid inside it, and condition (6) is satisfied over the complete surface, 
as well as any part of it. 

But turbulence in the motion will vitiate the principle that a 
bounding surface will always consist of the same fluid particles, 
as we see on the surface of turbulent water. 

24. To integrate the equations of motion, suppose the impressed 
force is due to a potential V, such that the force in any direction is the 
rate of diminution of V, or its downward gradient ; and then 

iVldz; (1) 



Putting 



x= 


= -dV/dx, Y 


= -dM/dy, Z 


and putting 

dw 
dy 


dv t 
-dz = 2 Z< 


du 

dz 


dw 
dx' 


= 2V, 


dv 
2* 






if. 
dx 


, dv ,<*{-. 
r 2y + dz~ 


=0, 



dy 2f> 



the equations of motion may be written 

du _ , ,dH 

- Tt -2vi+2wn+-^=o, 

dv t , _</H 

dw . „ . dH 

W -2UV + 2Vt + lr = 0, 



where 



H=fdp/ P +V+h<f, 
q* = u>+v 1 +w*, 



(2) 
(3) 

(4) 
(5) 
(6) 

(7) 
(8) 



JLu dv J.w . . /du . dv . dw\ . . 

^dx'^dx'^dx+^dx+d^+Tz)" ' ®> 



(10) 
(U) 

(12) 



and the three terms in H may be called the pressure head, potential 
head, and head of velocity, when the gravitation unit is employed 
and \q % is replaced by hq'/g. 

Eliminating H between (5) and (6) 

21 

dt *dx ''dx "dx~ r ' i \dx~ r dy 
and combining this with the equation of continuity 
1 Dp du . dv . dw 
p dt + dx + dy + dz~ ' 

we have g (?)- *^-2 * ?^ = 0> 

dt \p/ pdx pdx p dx ' 

with two similar equations. 
Putting 

a vortex line is defined to be such that the tangent is in the direction 
of u, the resultant of £, v, f, called the components of molecular 
rotation. A small sphere of the fluid, if frozen suddenly, would 
retain this angular velocity. 

If w vanishes throughout the fluid at any instant, equation (11) 
shows that it will always be zero, and the fluid motion is then called 
irrotalional; and a function <j> exists, called the velocity function, 
such that 

udx-\-vdy+wdz = -d<t>, (13) 

and then the velocity in any direction is the space-decrease or 
downward gradient of (j>. 

25. But in the most general case it is possible to have three 
functions <£, \[<, m of x, y, 2, such that 

udx+vdy+wdz = -d4>-md\f', (1) 

as A. Clebsch has shown, from purely analytical considerations 
{Crelle, lvi.) ; and then 



and 



H- 



d$ 



m lt= K > 



(4) 



dK 

■fa-2U$+2Wr,- 



■ =0, . 



, rf(«A, m) 1 d(^,m) „ i d(f,m) ,, 

* _i (J(y, Z )' *~»d(*. *)' f- '<J(*,y)' {) 

d<j/ d<lr , ji't' ydm , dm , jdm , . 

so that, at any instant, the surfaces over which i// and m are constant 
intersect in the vortex lines. 



=0, . 



(5) 



(6) 



(7) 



(8) 



the equations of motion (4), (5), (6) § 24 can be written 

d{<l/, m) 

d(x,t) ' 
and therefore 

Equation (5) becomes, by a rearrangement, 

dK._d\p/dm, dm. dm dm \ 

dx dH\dt +u dx + v dy +uh dT} 

, dm /dif/ , dii . dib , d\L\ 

+ d X -{M+ u -dx+ v d y : +w Tz) 

dKjfy Dm dm Dip _ 

{ dx dx dt + dx dt _0 ' • • •' 

and as we prove subsequently (§ 37) that the vortex lines are composed 

of the same fluid particles throughout the motion, the surface m and 

if/ satisfies the condition of (6) § 23 ; so that K is uniform throughout 

the fluid at any instant, and changes with the time only, and so 

may be replaced by F(/). 

26. When the motion is steady, that is, when the velocity at any 

point of space does not change with the time, 

dK , . , N 

-^-2t)f + 2«l7,=0 (1) 

JK . dK , JK dK . dK. dK , , 

^+'33r+ i '^ =0 ' u -dx-+ s !y- +w -dz-= ' < 3 > 

and 

rW<fM>+V+k 2 = H (3) 

is constant along a vortex line, and a stream line, the path of a fluid 
particle, so that the fluid is traversed by a series of H surfaces, each 
covered by a network of stream lines and vortex lines; and if the 
motion is irrotational H is a constant throughout the fluid. 

Taking the axis of x for an instant in the normal through a point 
on the surface H= constant, this makes u = o, { = ; and in steady 
motion the equations reduce to 

dH/dv = 2vt;—2wv — 2qws[nS, (4) 

where 6 is the angte between the stream line and vortex line ; and 
this holds for their projection on any plane to which dv is drawn 
perpendicular. 

In plane motion (4) reduces to 

*&+?)■ (5) 

if r denotes the radius of curvature of the stream line, so that 

Idp dvmdw = g\ \ 6) 

p dv dv dv dv r K ' 

the normal acceleration. 

The osculating plane of a stream line in steady motion contains 
the resultant acceleration, the direction ratios of which are 



dH 
-d7= 2( X- 



du , du , du d\q* ^ , dhq* dH 

u -Sx+ v J y + W -d-z = -dx- 2V >+™ r >=-Ix-Tx< 



(7) 



and when q is stationary, the acceleration is normal to the surface H 
= constant, and the stream line is a geodesic. 

Calling the sum of the pressure and potential head the statical 
head, surfaces of constant statical and dynamical head intersect 
in lines on H, and the three surfaces touch where the velocity is 
stationary. 

Equation (3) is called Bernoulli's equation, and may be interpreted 
as the balance-sheet of the energy which enters and leaves a given 
tube of flow. 

If homogeneous liquid is drawn off from a vessel so large that the 
motion at the free surface at a distance may be neglected, then 
Bernoulli's equation may be written 

H=p!p+z+qV2g = Plp+h, (8) 

where P denotes the atmospheric pressure and h the height of the 
free surface, a fundamental equation in hydraulics; a return has 
been made here to the gravitation unit of hydrostatics, and Oz is 
taken vertically upward. 

In particular, for a jet issuing into the atmosphere, where /> = P, 

g 2 /2g=/i-z, (9) 

or the velocity of the jet is due to the head k—z of the still free 
surface above the orifice; this is Torricelli's theorem (1643), the 
foundation of the science of hydrodynamics. 

27. Uniplanar Motion. — In the uniplanar motion of a homogeneous 
liquid the equation of continuity reduces to 
du , dv 



so that we can put 



dx+-dy-=°< 
u = — d^ldy , v = dt/dx, 



(1) 
(2) 



122 



HYDROMECHANICS 



[HYDRODYNAMICS 



where ^ is ? Junction of x, y, called the stream- or current-function ; 
interpreted physically, ^-^o. the difference of the value of ^ at a 
fixed point A and a variable point P is theflow, in ft. 3 / second, across 
any curved line AP from A to P, this being the same for all lines in 
accordance with the continuity. 

Thus if <ty is the increase of <fr due to a displacement from P to P', 
and k is the component of velocity normal to PP', the flow across 
PP' is fl^ = /fe.PP'; and taking PP' parallel to Ox, dil> = vdx; and 
similarly di-=~udy with PP' parallel to Oy; and generally d^fds 
is the velocity across ds, in a direction turned through a right angle 
forward, against the clock. 

In the equations of uniplanar motion 



rf£_i« _ dty , dfy 
2f dx dy ~ dx^dp 



-VV> suppose, 



so that in steady motion 

and vV must be a function of i£. 
If the motion is irrotational, 



d H , _, , dty 



3? 



+vV = o, 



dx dy' d~y dx' 



(3) 



(4) 



(5) 



so that 4> and <£ are conjugate functions of * and, y, 

<t>+*i=*f(x+yi), vV=o. v**=«o; (6) 

or putting 

<j>+\j/i=w, x+yi-z, w=f{z). 

The curves <t> = constant and 4> — constant form an orthogonal 
system; and the interchange of (j> and <// will give a new state of 
uniplanar motion,' in which the velocity at every point is turned 
through a right angle without alteration of magnitude. 

For instance, in a uniplanar flow, radially inward towards O, the 
flow across any circle of radius r being the same and denoted by 
2ittn, the velocity must be m/r, and 

tf>=mlogr, 4i=m$, ^-\-^i~m log re' 9 , vi—m log s. (7) 

Interchanging these values 

^ = mlcgr, <t> = m6, <J/+(t>i=m log re* e (8) 

gives a state of vortex motion, circulating round Oz, called a straight 
or columnar vortex. 

A single vortex will remain at rest, and Cause a velocity at any point 
inversely as the distance from the axis and perpendicular to Its direc- 
tion i analogous to the magnetic field of a straight electric, curneat. 

If other vortices are present, any one may be supposed to move 
with the velocity due to the others, the resultant streaniifiHvction 
being 

i£=fc2»z log r=log Mm; (9) 

the path of a vortex is obtained by equating the value of $ at the 
vortex to a constant, omitting the rm of the vortex itself. 

When the liquid is bounded by a cylindrical surface, the motion 
of a vortex inside may be determined as due to a series of vortex- 
images, so arranged as to make the flow zero across the boundary. 

For a plane boundary the image is the optical reflection of the 
vortex. For example, a pair of equal opposite' vortices, moving on 
a line parallel to a plane boundary, will have a corresponding pair 
of images, forming a rectangle of vortices, and the path of a vortex 
will be the Cotes spiral 

r sin 20 = 2<J, or x~^-\-y~' 1 — or"; . 4 ' . (10) 

this is therefore the path of a single vortex in a right-angled' corner; 
and generally, if the angle of the corner is ir/n, the path 19 the Cotes* 



a 
spiral 



r sin n$ = na. 



(»i 



and ^-f-Uy*^' is the stream function of the relative motion of the 
liquid past the cylinder, and similarly 4>~Vx for the component 
velocity V along Oy; and generally 

<-/ = vfr+Uy-V* (4) 

is the relative stream-function, constant over a solid boundary 
moVing with components U and V of velocity. 

If the liquid is stirred up by the rotation R of a cylindrical body, 

d^tds <= normal velocity reversed 



= -Rx' 



dx 
ds 



*y% 



(5) 



•A-HR^-hy'W, (6) 

a constant over the boundary; and 4 1 ' is the current-function of 
the relative motion past the cylinder, but now 

W'+2R=o, (7) 

throughput thejliquid. 

Inside an equilateral triangle, for instance, of height h, 

+' = - 2Rapy!h, ' (8) 

where a, 0, y are the perpendiculars on the sides of the triangle. 

In the general ease ^'=^-f-Uy- Vjc+JROtf-f-y 2 ) is the relative 
stream function for velocity components, U, V, R. 

39. Example 1. — Liquid motion past a circular cylinder. 
Consider the motion given by 

w=U(z+a«/z), (1) 



A single vortex in a circular cylinder of radius a at a distance c 
from the centre will move with the velocity due to an equal opposite 
image at a distance a 2 lc, and so describe a circle with velocity 

mcl(a*-r?)in the periodic time 2*(a*-c 2 )[m. (12) 

Conjugate functions can be employed also' for the motion of tiquicf 
in a thin sheet between two concentric spherical surfaces; the com- 
ponents of velocity along the meridian and parallel in colatitude 8 
and longitude X can be written 

d4 = i_ d$ 1 djj> _ djj fiii 

de = sin 8 d\' sin d\ " d6' { 3; 

and then 

4> + ^ i = F (tan \8. «*•') . (14) 

28. Uniplanar Motion of a Liquid due to the Passage of a Cylinder 
through it. — A stream-function <f must be determined to satisfy the 
conditions 

VV = o, throughout the liquid; ■ (1) 

4> -constant, over any fixed boundary ; (2) 

d^/ds =• normal velocity reversed over a solid boundary, (3) 

so that, if the solid is moving with velocity U in the direction Ox, 
di>lds— — Vdy/ds, or ^+U> = constant over the moving cylinder; 



so that 



^ = u(r+7)cos9=u(i+^)*, 
^Tj(,-f)sin0 = u(i-g)y. 



(2) 



Then 4/ = over the cylinder r = a, which may be considered a fixed 
post; and a stream line past it along which ^ = Uc, a constant, is 
the curve 

■ \ (3) 

a cubic curve (C3). 

Over a concentric cylinder, external or internal, of radius r = b, 



I r - —) sin 6 =>c, (* 5 +y 2 )(y-c) -o 2 y = o, 

.). 

ric cylinder, 1 

*W+U,y-lu(i-g|)+Ui]y, 



(4) 



and $' is zero if 

Ui/U = (a 2 -frW; (5) 

so that the cylinder may swim for an instant in the liquid without 
distortion, with tb,is velocity Ui; and w in (1) will give the liquid 
motion in the, interspace between the fixed cylinder r = o and the 
concentric cylinder r = 6, moving with velocity Ui. 

When 6 = 0, Ui=oo; and when 6 = 00, Uj=>-U, so that at 
infinity the liquid is streaming in the direction *0 with velocity U. 

If the liquid is reduced to rest at infinity by the superposition of 
an opposite stream given by 10= — Uz, we are left with 

. «- = Ua 2 /z, (6) 



</> = U(a 2 /r) cos 8 = Ua'x/(x*+f), 
i*** -U(a 2 /r) sin = -Va'y/ix'+f), 



(7) 
(8) 



giving the motion due to the passage of the Cylinder r = a with 
velocity U through the origin O in the direction Ox. 
If the direction of motion makes an angle 8' with 0#, 



d(j> jd4> _2xy 



tan9 ' = Ty/^=^ 



f 



= tan 28, 8 = is', 



and the Velocity is Ua J /r 2 . 
. Along the path of a particle, defined by the C 3 of (3), 

_ y(y-c) 

x i + y i o 2 • 



sin 2 \8' = 



. . .,d0' iy -cdv 



(9) 



(JO) 



(») 



on the radius of curvature is Ja 2 /(y — %c), which shows that the curve 
is an Elastica or Lintearia. (J. C. Maxwell, Collected Works, ii. 208.) 
If <fo denotes the velocity function of the liquid filling the cylinder 
r = b, and moving bodily with it with velocity Ui, 

«fr=-Ui*, (12) 

and over the separating surface r = b 

a? + V 



* _ U / , , o 2 \ 



.¥' 



(13) 



and this, by § 36, is also the ratio of the kinetic energy in the annular 
interspace between the two cylinders to the kinetic energy of the 
liquid moving bodily inside r = b. 

Consequently the inertia tc overcome in moving the cylinder 
r — b, solid or liquid, is its own inertia, increased by the inertia of 
liquid (a 2 +S 2 )/(a'~6 2 ) times the volume of the cylinder r — b; 
this total inertia, is called the effective inertia of the cylinder r^b, 
at the instant the two cylinders are concentric. 



HYDRODYNAMICS] 



HYDROMECHANICS 



123 



(14) 



With liquid of density p, this gives rise to a kinetic reaction to 
acceleration dV/dt, given by 

..a'+WdU a?+b\.,dV 
Tpb a^WdT = "a^¥ M Si' 

if M' denotes the mass of liquid displaced by unit length of the 
cylinder r = b. In particular, when o = 00 , the extra inertia is M'. 

When the cylinder r = a is moved with velocity U and r = 6 with 
velocity U, along Ox, 



<t> = U 



a 2 /6 s \ b f I a*\ 

j^(7 + r)cos9-U 1 rr^(r + 7 jcos<>, (»5) 

r~{j~r) s ine-\J l¥ ^(r-f)sin$-, (t6) 



and similarly, with velocity components V and Vi along Oy 

V 



<(•-- 



Vrj^^+^sino-v,^ 



Isin8-Vn 



*K) 



sinfi, 



*= V^(£-r)co.«+V^(r-£)coB»; 



(17) 
(IS) 



and then for the resultant motion 



w= (U 2 + V*)j 

-(Ui»+Vi»)j: 



+ 



a* U +Vi 



6 2 a 2 2 
a'6' U1+V1* 



; 6 2 -a 2 U+Vi 

&' S "'"" "ITVH , Irv s 

The resultant impulse of the liquid on the cylinder is given by the 
component, over r = a (§ 36), 

t 6 2 +a 2 TT 2b 2 



-U, 



2 b 2 V 

! - aV '• 



-U 



X =fp<t> cos 6. add = irpa 2 (u 55- 

and over r = 5 

X, =ffxt>cosB.bdd = xpb 2 /u 5^ 

and the difference X-Xi is the component momentum of the liquid 
in the interspace ; with similar expressions for Y and Yi. 
Then, if the outside cylinder is free to move 

Y V, 2a 2 Y ,„V " 2 

Ai=o, Tr = M_L.„2' -X. = 7rpa-U 






-a 2 )' 



(20) 



(21) 



U P-fa 2 ' "-""■-"&+&• 

But if the outside cylinder is moved with velocity Ui, 
inside cylinder is solid or filled with liquid of density a, 

2pV> 



X = 



-TrirafV, -ft 



p(6 2 +a 2 )+o'(6 s -a s 
U-U. ._ (p-g)(y-a') 
Ui -p(V+a*)'+<,{&-a?)> 



(22) 
and the 



(23) 



to space filled with liquid, and at rest at infinity, the cylinder will 
experience components of force per unit length 
(i.) —2TpmV, 2irpwU, due to the vortex motion ; 

(ii.) — irpa 2 -T7-, —xpo?-37, due to the kinetic reaction of the liquid; 

(iii.) o, —r(<r—p)a 1 g, due to gravity, 
taking Oy vertically upward, and denoting the density of the cylinder 
by <r; so that the equations of motion are 



and the inside cylinder starts forward or backward with respect to 
the outside cylinder, according as p> or <<7. 

30. The expression for w in (1) § 29 may be increased by the 
addition of the term 

i'm log z=~mB -f im log r, (1) 

representing vortex motion circulating round the annulus of 
liquid. 

Considered by itself, with the cylinders held fixed, the vortex 
sets up a circumferential velocity m/r on a radius r, so that the 
angular momentum of a circular filament of annular cross section dA. 
is pmd.\, and of the whole vortex is pmr(b 2 — a?). 

Any circular filament can be started from rest by the application 
of a circumferential impulse rpmdr at each end of a diameter; so 
that a mechanism attached to the cylinders, which can set up a 
uniform distributed impulse irpm across the two parts of a diameter 
in the liquid, will generate the vortex motion, and react on the 
cylinder with an impulse couple— pmira 2 and pmjri 2 , having re- 
sultant pm7r(6 2 — a 2 ), and this couple is infinite when b = 00 , as the 
angular momentum of the vortex is infinite. Round the cylinder 
r =0 held fixed in the U current the liquid streams past with velocity 

}'=2U s'me+m/a; (2) 

and the loss of head due to this increase of velocity from U to q' is 

1*~ U " _ < 2lJ sin e + m l a ) i - U 8 

2g 2g 

so that cavitation will take place, unless the head at a great distance 
exceeds this loss. 

The resultant hydrostatic thrust across any diametral plane 
of the cylinder will be modified, but the only term in the loss 
of head which exerts a resultant thrust on the whole cylinder,, is 
2mU sin 6/ga, and its thrust is 2xpmU absolute units in the direction 
Cy, to be counteracted by a support at, the centre C; the liquid is 
streaming past r = a with velocity U reversed, and the cylinder is 
surrounded by a vortex. Similarly, the streaming velocity V 
reversed will give rise to a thrust 2xp»»V in the direction xC. 

Now if the cylinder is released, and the components U and V are 
reversed so as to become the velocity of the cylinder with respect 



(3) 



jrfU 

1 dt 



= - irpa' 



„dV_ 
dt 



2-rpmV, 



JV 2 iV . .. . ■ . , 



(4) 
(5) 



or, putting jm = <j 2 co, so that the vortex velocity is due to an angular 
velocity a at a radius a, 

(<r+p)dVldt+2puV=o, (6) 

(a+p)dV/dt-2pwU + (<T-p)g = o. (7) 

Thus with g = o, the cylinder will describe a circle with angular 
velocity 2p«/(ffrt-p) 1 so that the radius is (a+p)v/2pa, if the velocity 
is v. With o-*=o, the angular velocity of the cylinder is 2a>; in this 
way the velocity may be calculated of the propagation of ripples 
and waves on the surface of a vertical whirlpool in a sink. 

Restoring a will make the path of the cylinder a trochoid; and 
so the swerve can be explained of the ball in tennis, cricket, base- 
ball, or golf. 

Another explanation may be given of the sidelong force, arising 
from the velocity of liquid past a cylinder, which is encircled by a 
vortex. Taking two planes x — =*= b, and considering the increase of 
momentum in the liquid between' them, due to the entry and exit 
of liquid momentum, the increase across dy in the direction Oy, 
due to elements at P and P' at opposite ends of the diameter PP', is 
pdy (U ■ — UaV -2 cos 2 0+mr _1 sin ^(UoV -2 sin 2 e+mr~ l cosfl) 

-f pdy ( — U+UaV -2 cos2 0+«r~ 1 sin0)(UaV~ 2 sin20 — mr~ l cosS) 

=2pdymtJr- l (.cos6— a, 2 r^ cos 30), '(&)'' 

and with y = b tan 6, r = b sec 9, this is 

2pmVd$(i— a'b-^coB 36 cos 6), (9) 

and integrating between the limits 6= ± 5T, the resultant, as before, 
is Ijrpmtj. 

31. Example 2. — Confocal Elliptic Cylinders. — Employ the elliptic 
coordinates n, |, and f = i;+|t, such that 

2=cchf, x = ccht) cos f, y — cshti sin£; (1) 

then the curves for which i\ and { are constant are confocal ellipses 
and hyperbolas, and 

= §c 2 (ch2i) — cos2£)=rir 2 = OD 2 , (2) 

if OD is the semi-diameter conjugate to OP, and n, r% the focal 
distances, 

n,r 2 = c(ch)j±cos£); (3) 



r* = x 2 +y- = c 1 (ch ! 7j - sin 2 ?) 



(4) 



= sC ! (ch2»;+cbS2j). 
Consider the streaming motion given by 

w = mch(f—y), 7 = a+/3i, (jj) 

<p = mch(i) — a)cos({ — 0), ^ = msh(ij — o)sin({— 0). (6) 

Then ^ = over the ellipse i) = o, and the hyperbola £ = /S, so that 
these may be taken as fixed boundaries ; and ^ is a constant on a C4. 
Over any ellipse ij, moving with components U and V of velocity, 
' ^'=^4-Uy-V»f = [wsh(ij-a)cos/3-fUcshii]sm£ 

— [msh(ri — o) sin/3+Vcch7j] cos £; (7) 
so that \j/' = o. if 



tt— m shQ? - a) 



sh 1 



cos V= -~ 



m sh(7) - a) 



ch 1 



sin/3, 



(8) 



having a resultant in the direction PO, where P is the intersection of 
an ellipse r> with the hyperbola /3; and with this velocity the ellipse 
ij can be swimming in the liquid, without distortion for an instant. 
At infinity 



Tj = --e "cos /S = -^TTjCOS /3, 



V = 



e _<, sin /3 = ■ 



a + b 



sin (S, 



(9) 



a and 6 denoting the semi-axes of the ellipse o; so that the liquid is 
streaming at infinity with velocity Q=m/(a+b) in the direction of 
the asymptote of the hyperbola /3. 

Art ellipse interior to r/ = a will move in a direction opposite to 
the exterior current ; and when 17 = o, U = 00 , but V = (m/c) 1 sh a sin 0. 

Negative values of ri must be interpreted by a streaming motion 
on a parallel plane at a level slightly different, as oil a double Riemann 
sheet, the 'Stream passing from 6ne: sheet to the other across a cut 
SS' joining the foci S, S'. A diagram has been drawn by Col. P.. L. 
Hippisley. 



124 



HYDROMECHANICS 



[HYDRODYNAMICS 



The components of the liquid velocity q, in the direction of the 
normal of the ellipse ij and hyperbola £ , are 

-wJ- 1 sh(^o)cos(t-(S),wJ-»ch(^-o)sin(^). do) 

The velocity q is zero in a corner where the hyperbola /S cuts the 
ellipse a; and round the ellipse a the velocity g reaches a maximum 
when the tangent has turned through a right angle, and then 



„ V (ch 2a-cos 20) 

s = Q ea sFi^ — • 



(II) 



and the condition can be inferred when cavitation begins. 
With = o, the stream is parallel to *o, and 
<£ = »»cb(T*a)cos£ 
= - Uc ch (ij-a) sh ij cos £/sh (17-0) (12) 

over the cylinder ij, and as in (12) § 29, 

<fr=-Ua; = -U£chijcos £, (13) 

for liquid filling the cylinder; and 

* = tni > 
<tn~ ' 



(H) 



th (,-<.)• 

over the surface of 1;; so that parallel to Ox, the effective inertia 
of the cylinder 7/, displacing M' liquid, is increased by M'thi>/th(t)«a), 
reducing when = 00 to M' thij = M'(fr/o). 

Similarly, parallel to Oy, the increase of effective inertia is 
M'/th 17 th(i7-o), reducing to M'/th ij = M'(a/&), when = 00 , and 
the liquid extends to infinity. 

32. Next consider the motion given by 

= wch 2(j)-a)sin2{, ^ = -w sh 2(i»-a)cos 2£; (1) 

in which ^=0 over the ellipse a, and 
fa=++hR(x 2 +?) 

= [-j»sh2(ij-a)+JRc 2 ]cos2{+|Rc ! ch2rj, (2) 
which is constant over the ellipse tj if 

iRc 2 = msh 2(1,-0); (3) 

so that this ellipse can be rotating with this angular velocity R for 
an instant without distortion, the ellipse o being fixed. 

For the liquid filling the interior of a rotating elliptic cylinder of 
cross section 

x* la* +?l& = i, (4) 

fa'=miWa*+y*/b') (5) 

with vVi'=-2R=-2Wi(i/o 2 +i/& 2 ;, 

*i =m(x'/a*+y'lb*) - iR(x 2 +f) 

^~iR(x 2 -y 2 )(a 2 -b 2 )/(a 2 +b 2 ), (6) 

fa = Rxy(a 2 -o 2 )l(a 2 +b 2 ), 
Wi=fa+fai = - hiR(x+yi)*(a 2 -P)/(a 1 +b i ). 
The velocity of a liquid particle is thus (a 2 — £> 2 )/(a 2 +6 2 ) of what 
it would be if the liquid was frozen and rotating bodily with 
the ellipse; and so the effective angular inertia of the liquid is 
(a 2 — fc 2 ) 2 /(a 2 +6 2 )' of the solid; and the effective radius of gyration, 
solid and liquid, is given by 

* 2 = i(a 2 +& 2 ),andK<* 2 -& J )7(a 2 +* 2 ). (7) 

For the liquid in the interspace between o and tj, 

<j>_ m ch 2fa-a) sin 2f 

fa ~ JRc 2 sh 2r, sin 2^(0? - b 2 )!(a 2 +b 2 ) 

= i/th2(jra)th2i;; (8) 

and the effective k 2 of the liquid is reduced to 

!c 2 /th2(>j-a)sh2i|, (9) 

which becomes }c 2 /sh 2ij = J(o*-6*)/a6, when = 00, and the liquid 
surrounds the ellipse ij to infinity. 

An angular velocity R, which gives components — Ry, Rx of 
velocity to a body, can be resolved into two shearing velocities, — R 
parallel to Ox, and R parallel to 0> ; and then \p > s resolved into 
^1+^2, such that ^-1 + jRc 2 and fa+^Ry 2 is constant over the 
boundary. 

Inside a cylinder 

fa+fai = - JiR(*+yi) 2 <i 2 /(a 2 +6 2 ), (10) 

«*+**» = iiR(x+yi) 2 b 2 l(a 2 +b 2 ), (11) 

and for the interspace, the ellipse o being fixed, and 01 revolving 
with angular velocity R 

fa+fai = -|i'Rc 2 sh2(»j-a+Jj)(ch2o+l)/sh2(ai-o), (12) 
<h+fai = s«Rc 2 sh2(ij-a+{i)(ch2o-l)/sh2(ai-a) ( (13) 
satisfying the condition that fa- and <p% are zero over tj = o, and over 

^+£R* 2 = iRc 2 (ch 20.1 + 1), (14) 

^+|Ry 2 = iRc 2 (ch2a 1 -i), (15) 

constant values. 

In a similar way the more general state of motion may be analysed, 
given by 

W = wch2(f— 7), 7 = a+/3i, (16) 

as giving a homogeneous strain velocity to the confocal system; 
to which may be added a circulation, represented by an additional 
term i»f in v>. 



Similarly, with 
the function 



X+yi=H[sin(£+mi)] 



(17) 



*=QcshlO,-a)sini(£-<8) (18) 

will give motion streaming past the fixed cylinder ij = a, and dividing 
along 4 = /S; and then 

x 2 — y 2 =c t sinjchij, 2ry = e 2 cos£ shij. (19) 

In particular, with sh o = I , the cross-section of 7; = o is 

x*+6x 2 y i +y*=2c i , or x i +y 4 =c* (20) 

when the axes are turned through 45°. 

33. Example 3. — Analysing in this way the rotation of a rectangle 
filled with liquid into the two components of shear, the stream 
function fa is to be made to satisfy the conditions 

(i.)vVi=o, 

(ii.) fa-\-$Rx 2 = iRa 2 , or f =owhenj= =*=a, 

(iii.) fa + iRx 2 = hRa 2 , ^ 1 = |R(a 2 -x 2 ), when y= ±6 

Expanded in a Fourier series, 

a , . 32 ,-Sp cos(2n+i)Wa , . 

° * 7T 3 ° Z~i (2M + I) 3 ' u > 

so that 



. _ p l6 ,X~* C0 s(2«+l)^7rx/q . ch(2»+i)|iry/a 
*' 1-K 7r 3a 2*~ (2n+i) 3 .ch(2n+i)^7rfe/a ' 
x , , . .,,16 ,^T^ . cos(2n+i)j7rz/a_ 
w^fa+fa—iR^a 2^(2»+i) 3 ch(2» + l)ix6/a' 



(2) 



an elliptic-function Fourier series; with a similar expression for ^2 
with x and y, a and 6 interchanged; and thence <p = fa+fa. 

Example 4. — Parabolic cylinder, axial advance, and liquid stream- 
ing past. 

The polar equation of the cross-section being 

rlcos §0 = ah, orr + x=2a, (3) 

the conditions are satisfied by 

fa = Vr sin 6 -2\JaM sin J9 =2tM sin §e(ri cos \B - ah), (4) 
* = 2Uairisinit? = -UV[2a(r-*)], (5) 

w=-2Ua5zJ, (6) 

and the resistance of the liquid is 2xpoV 2 /2g. 

A relative stream line, along which fa = Vc, is the quartic curve 
4 a , y 2 -(y-cy ,,_ 4aV+(y-c) i 
4o(y-<;) 2 ' 



y-c = V[2o(r-*)], 



\ayy-cy ' " 
and in the absolute space curve given by fa. 

dy_^ (y - c) 2 
dx 2ay ' 



(7) 



2ac . , .. 
^=— — -2alog(y-c). 



(8) 



34. Motion symmetrical about an Axis. — When the motion of a 
liquid is the same for any plane passing through Ox, and lies in the 
plane, a function ^ can be found analogous to that employed in 
plane motion, such that the flux across the surface generated by the 
revolution of any curve AP from A to P is the same, and represented 
by 27r(^— ^0); and, as before, if dip is the increase in ^ due to a 
displacement of P to P', then k the component of velocity normal 
to the surface swept out by PP' is such that 27r<fy' = 27ry&.PP'; and 
taking PP' parallel to Oy and Ox, 

u = — dfalydy, v = d-^lydx, (1 ) 

and f is called after the inventor, "Stokes's stream or current 
function," as it is constant along a stream line (Trans. Camb. Phil. 
Soc, 1842; "Stokes's Current Function," R. A. Sampson, Phil. 
Trans., 1892); and d<f/jyds is the component velocity across ds in a 
direction turned through a right angle forward. 
In this symmetrical motion 

,. d (ld$\ , d(ld^\ 
£ = 0, , = 0, Jf-jj^jj) +fi{- Ty ) 

= l(i± d^^dfa, 1 
y\dx 2 ^dy i ydy) y v ^' 



suppose; and in steady motion, 

dH , 1 dfa^,, rfH ,1 dfa.. 

dl+y-*lx v ^ = °' ■Sy- + 5 2 3y v ^ =0 ' 
so that 

2f/y=- y^vV = dH/dip 
is a function of fa. say /' (fa, and constant along a stream line; 

dH/dt> = 2qt, H-/(^)= constant, 
throughout the liquid. 

When the motion is irrotational, 

dQ^ldj, 
dy y dx' 



d<t> 1 &p 
f =0 - u= -Tx = —yTy "=- 



V**« 



dV , d 2 ^ 1 df 



°' or oV+3? 



y dy' 



(2) 

(3)- 

(4) 

(5) 

(6) 
(7) 



HYDRODYNAMICS] 



HYDROMECHANICS 



Changing to polar coordinates, * = r cos 6, y = r sin ft, the equation 
(2) becomes, with cos ft=/i, 



!25 



'■fgH-cl-rtg-'i**' 



(8) 



of which a solution, when f = 0, is 

*- (*"*+5) d-^-(A^+^) /£, (9) 

<^ = [(n + i)Ar»-nBr-»- 1 lP n , (10) 

where P„ denotes the zonal harmonic of the nth order; also, in the 
exceptional case of 

^ = A cos ft, <t> = A /r; 

t = B r, <t> = - B log tan %0 

= -JB sh- 1 x/y. (11) 

Thus cos 8 is the Stokes' function of a point source at O, and 
PA- PB of a line source AB. 

The stream function tp of the liquid motion set up by the passage 
of a solid of revolution, moving with axial velocity U, is such that 

yTs = -V% * + * U ?' constant, (12) 

over the surface of the solid ; and ^ must be replaced by^-' = <//+ |U}> 2 
in the general equations of steady motion above to obtain the steady 
relative motion of the liquid past the solid. 

For instance, with n = i in equation (9), the relative stream 
function is obtained for a sphere of radius a, by making it 

^'=^ + iUy = |U(r 2 -o 3 /r)sin 2 e, + = -iUa> sin 2 ft/r; (13) 
and then 

0' = U*(i+§a 3 /r 2 ), <*> = JUa 3 cosft/r 2 , (14) 



d<t> IT* 1 * a dd> nid 1 . „ 



(15) 

so that, if the direction of motion makes an angle ^ with O*, 

tan W--£)=Jtanfl, tan ^ = 3 tan ft/(2 -tan 2 ft). (16) 

Along the path of a liquid particle <j/' is constant, and putting it 
equal to JUc 4 , 

_(r 2 -a J /V) sin 2 ft=c 2 , sin 2 9=c 2 r/(r 3 -<j 3 ), (17) 

the polar equation; or 

y = c 2 r 3 /(r 3 -a 3 ), r' = a 3 y i l{f-c 1 ), (18) 

a curve of the 10th degree (C10). 
In the absolute path in space 
cos ^ = (2-3sin 2 0)/V(4-sin s «),andsin , « = (y»-c*y)/o>, (19) 
which leads to no simple relation. 

The velocity past the surface of the sphere is 

1 <¥' itt/', ,a 3 \sin 2 ft , TT . „ . , . 

so that the loss of head is 

(J sin 2 ft — i)U 2 /2g, having a maximum |U 2 /2g, (21) 
which must be less than the head at infinite distance to avoid 
cavitation at the surface of the sphere. 

With n — 2, a state of motion is given by 

^-JU/aV/r 4 , ^' = |Uy 2 (i-aV 4 ), (22) 

<t>' = Ux+<t>, <*>=-£U(aV 3 )P2, P. = fAi'-i, (23) 

representing a stream past the surface r* = a*p. 

35. A circular vortex, such as a smoke ring, will set up motion 
symmetrical about an axis, and provide an illustration; a half 
vortex ring can be generated in water by drawing a semicircular 
blade a short distance forward, the tip of a spoon for instance. 
The vortex advances with a certain velocity; and if an equal 
circular vortex is generated coaxially with the first, the mutual 
influence can be observed. The first vortex dilates and moves 
slower, while the second contracts and shoots through the first; 
after which the motion is reversed periodically, as if in a game of 
leap-frog. Projected perpendicularly against a plane boundary, 
the motion is determined by an equal opposite vortex ring, the 
optical image; the vortex ring spreads out and moves more 
slowly as it approaches the wall; at the same time the molecular 
rotation, inversely as the cross-section of the vortex, is seen to 
increase. The analytical treatment of such vortex rings is the 
same as for the electro-magnetic effect of a current circulating 
in each ring. 

36. Irrotational Motion in General. — Liquid originally at rest in 
a singly-connected space cannot be set in motion by a field of force 
due to a single- valued potential function; any motion set up in 
the liquid must be due to a movement of the boundary, and the 
motion will be irrotational ; for any small spherical element of the 
liquid may be considered a smooth solid sphere for a moment, and 
the normal pressure of the surrounding liquid cannot impart to it 
anv rotation. 



The kinetic energy of the liquid inside a surface S due to the 
velocity function </> is given by 






(1) 



by Green's transformation, dv denoting an elementary step along 
the normal to the exterior of the surface ; so that d$jdv = o over 
the surface makes T = o, and then 

[Tx) + W +U> °' Tx =0 ' Ty=°' Tz =0 - V 
If the actual motion at any instant is supposed to be generated 
instantaneously from rest by the application of pressure impulse 
over the surface, or suddenly reduced to rest again, then, since no 
natural forces can act impulsively throughout the liquid, the pressure 
impulse a satisfies the equations 



1 da 



pdx 



= -u, 



-os, 



(3) 



1 da_ _ 1 da 
P dy ' ~ p ~dz' 
c = p^>+a constant, (4) 

and the constant may be ignored; and Green's transformation of 
the energy T amounts to the theorem that the work done by an 
impulse is the product of the impulse and average velocity, or half 
the velocity from rest. 

In a multiply connected space, like a ring, with a multiply valued 
velocity function <p, the liquid can circulate in the circuits inde- 
pendently of any motion of the surface; thus, for example, 

<t> = m6 = m ta.n~ l y/x (5) 

will give motion to the liquid, circulating in any ring-shaped figure 
of revolution round Oz. 

To find the kinetic energy of such motion in a multiply connected 
space, the channels must be supposed barred, and the space made 
acyclic by; a membrane, moving with the velocity of the liquid; 
and then if k denotes the cyclic constant of <t> in any circuit, or the 
value by which <f> has increased in completing the circuit, the values 
of </> on the two sides of the membrane are taken as differing by k, 
so that the integral over the membrane 



ff&->ff&>- 



(6) 



and this term is to be added to the terms in (1) to obtain the ad- 
ditional part in the kinetic energy; the continuity shows that the 
integral is independent of the shape of the barrier membrane, and 
its position. Thus, in (5), the cyclic constant k = 2Trm. 

In plane motion the kinetic energy per unit length parallel to Oz 

-Itfifc-bftgi,. ( 7 ) 

For example, in the equilateral triangle of (8) § 28, referred to co- 
ordinate axes made by the base and height, 

r = -2RaPy/h = - iRyl(h-y)*-3x*]lh (8) 

^-mW + iWy+h^-y^-yc'y+yyh (9) 

and over the base y = o, 

dx\dv = -dx/dy = +iR(ih?-3x*)/h,+ = - \R(\W-\-x*). (10) 

Integrating over the base, to obtain one-third of the kinetic 
energy T, 

= P IW/i35V3 (11) 

so that the effective k? of the liquid filling the triangle is given bv 
* 2 =T/J P R 2 A = 2^/45 * b s X 

= | (radius of the inscribed circle) 2 , (12) 

or two-fifths of the A 2 for the solid triangle. 
Again, since 

d4ldv = d^jis, d<j>jds= -d<///di>, (13) 

T = Ipftdf = - \ptyd4. (14) 

With the Stokes' function ^ for motion symmetrical about an 
axis. 

T = ipj4> -^firyds = rpffrlf. \i 5 ) 

37. Flow, Circulation, and VorUx Motion.— -The line integral of 
the tangential velocity along a